Is the writing intuitive? Are any concepts difficult to grasp?

The presentation of your website looks basically alright, but it seems your format is to start with the problem, go through a bit of a story, explain concepts of voting methods, and then wind up with the solution at the end. That works for some contexts but in a more academic or technical flavored setting, and what I find easier to work with, is to start with the thesis upfront and then unpack it with details lower down. The blogging/rhetorical style is understandable for the front page of the website, but when I click the link to the chapter Persistent Democracy, there at least I expect to immediately jump into a snappy description of what you are proposing. Something like:

"In Persistent Democracy, scheduled elections will be replaced by ______ where voters can _____. This will solve the problems of ______, _______, and ______, by ______ and _____. " Hope you get the idea.

As it stands, I'm a little unsure what you're proposing because on one hand you say it will enable direct democracy but on the other hand you talk about how politicians such as mayors might be elected with your system.

Does the concept seem robust and useful enough that it's worth experimenting with? Are there any serious problems I haven't addressed? Does the book make a compelling and persuasive argument?

I've only looked at a few parts of your website so far, so don't take this as an attack, but a description of my current views so that you can know the challenge of what you'd have to do to overcome my skepticism. I support representative democracy over direct democracy. I think that in some cases, bureaucratic experts should have a bit more power. I think America currently has on average too much public scrutiny of government projects. I am wary of political systems which too heavily reward participatory effort, because it can give too much power to a vocal and well-resourced minority, as we see with NIMBY groups opposing upzoning. I think that people who are very informed and engaged in politics are not necessarily better voters because their knowledge and passion usually comes alongside heightened bias and radicalism. I think that Congress works better when the public doesn't pay close attention to it. I think that recall elections, such as those I observe in my state of California, are a bad system. And at least some EAs who are plugged into politics largely agree with these points (indeed, several of the above citations come from EAs). Putting it all together, this is a less populist point of view which makes me skeptical about your approach.

You also should probably address the question of whether your voting system would be secure when it seems to require electronic voting. I gather that many informed people are very skeptical about the security of electronic voting. I see that you say something about the need to make safe software, but that aspiration won't be enough to convince election experts that such software actually will exist. And by the way, if you can describe the way to make provably correct, hacker-proof voting software, that alone is very impressive and should be presented somewhere else as a big idea in its own right, not just included as a component of this voting reform project. But, cards on the table, I am by default very skeptical of any claim that someone can make such foolproof software. In general, if your idea requires simultaneous breakthroughs or reforms at the same time, it all gets that much harder. Maybe there's a 30% chance of persuading people that your voting idea is theoretically desirable, and a 30% chance of the right software being available, well then the chance of success is only 9%. If you can sketch out governance reforms which don't simultaneously require a breakthrough in software development, they will be more plausible.

I'll admit for context that I’m not personally convinced by your argument. I'm in the less but better camp on fixing democracy, not the more and often camp. More democracy, more often doesn't really fix the biggest issues with democracy as it stands (populism, low levels of policy understanding, desire satisfaction short-termism, politicians not having enough time to actually deliver policy agendas before the hounds are set on them for not delivering and they are subsequently voted out, niche powerful interest groups being overrepresented...)

That being said I think this is a really interesting direction to explore - and have a lot of respect for the significant amount of time it is clear you've invested into this project.

My biggest takeaway from your amended webpage (the one linked at the top) is that it still really needs a ‘This is what Persistent Democracy would mean in practice and this is how it would change your day-to-day life’ section right at the start. Your writing is incredibly rich in its exploration of PD in relation to specific causes you regard as important but I really needed an early grounding without having to skim through to understand it. Hard to effectively evaluate your arguments otherwise. Clear that you've understood your most likely critics and created clear distance between yourself and obvious contemporaries.

Would be interesting to see how this fits with the other big trend in the more and often camp of democracy fixing which is arguments for people’s assemblies and more direct referendums.

It was easy for me to grasp because I've read about similar stuff before. 

There are some serious issues that were not addressed. 

Content warning: Very dark and depressing stuff. 
The voting system does not address culture. Voting or changing your mind on issues does not address the cultural attitudes that are pro-abuse, pro-violence, pro-corruption. Laws and legislators are meaningless without a culture that backs it up.  That's why there's so many countries with very progressive laws and constitutions, yet have regular horrendous human rights violations.  This voting system in the United States would no doubt spark genocide. Our economy is set up in a way that attacks people's time, especially minorities. Republicans and wealthy people have so much power because they have lots of free time to spew their hatred into tangible policy that gets passed, and they have plenty of time to waste rejecting solutions that would improve people's quality of life. Some of our longest filibusters have been rejecting laws that enforced human rights.  Our propoganda is so severe that it would be a fast-track people voting against themselves. Politicians in some sense provide a buffer from allowing people to commit political suicide. (from the standpoint of food stamps and healthcare, suicide is very literal.) Yes, there are people who don't support our government's actions today. But they don't vote. I think the statistics on the number of non-supporters isn't accurate either- if they measure what people support but don't measure how blindly they answer yes to every survey question then the survey doesn't mean much. 

For the US,  someone could say that this is caused by bad politicians. But the farther you go back, the worse it gets. Bigger massacres, violence against all minorities significantly more socially acceptable, greater premature death. In the civil war you had people who would rather die and/or murder their own family members than free their slaves. That's not an evil politician issue. That's an evil people issue.

This also doesn't address people's opinions being shaped by their brain chemistry. People have longer lifespans now, which swings politics conservative. People get conservative when they age because their brain isn't as functional. They don't want change because change takes effort for them to process. Older people have much more time on their hands to vote. Stress and other conditions impact people's political views, that's why there's a link between CPTSD and political extremism.