Here's the story. I've been using Aquari-sol for years as a weekly preventative.
This is your culprit right here. The reason it is not working is because you've successfully cultured yourself a colony of aquari-sol resistant bugs. The weekly "good luck charm" may have killed off the vast majority of the bugs each week, but if only a few survived -- the few that naturally would be slightly more immune to the medication than the rest of its mates -- then they grew and when the next week's "good luck charm" was dosed again the resistant ones would survive.
Over time, you've created a colony that has been bred specifically to be resistant to that medication. Especially since ich's lifecycle is only about 3 days at tropical temperatures!
Another example of is the overuse of antibiotics that as created strains of bacteria that are resistant to darn near everything. Staph infections used to annoying infections you'd get sometimes in the hospital, but they were curable and that was that. Today, if you get a staph infection, you better hope and pray that it isn't one of those strains that are virtually invulnerable to all known medications.
There is no medication you or your pets need as a "preventative". (Unless of course, prescribed to you by an M.D. or vet for a legit medical reason.) The consequences are that the bugs that cause the diseases very easily adapt and spread that acquired immunity around.
To cure your problem, you need to find an ich medicine that doesn't have the same ingredients as the aquari-sol you have been using.
I also sincerely hope that you will take up the responsibility to do your absolute best to make sure that the strain you have cultured there doesn't get out. That you will never share fish from that tank with others, and you will never share plants or decorations or equipment from that tank unless they are thoroughly dried out (ich cannot survive being dried out) or they sit in a completely fish-free tank for several weeks (again, ich's life cycle is about 3 days at tropical temperatures and they have to have fish to parasatize off of to survive, so no fish in the tank = no ich). It would even be nice if you took special care of the water you take out of the tank -- specifically, don't just send it down the drain if you can help it. If you can pour it on the ground or somewhere else there is zero chance of it getting to fish, that would be best. The goal here is to try to keep these bugs out of the water system where it may reach any fish at any point.
I certainly can't make you do this, but I can ask that you try. It would be really, really good for the aquarium community if this strain did not get out and be resistant to one of the more potent medicines at our disposal.
I'd also ask you to read through this page:
http/www.skepticalaquarist.com/docs/health/ich.shtml which is the best resource about ich I have ever seen on the web. There is talk in there about strains that have other kinds of resistance -- like some strains that are resistant above 90 *F today -- and talks about why you need to understand the lifecycle of ich to know how to treat your tank effectively. It also addresses many of the common myths and truths about ich. If you have any questions, please don't hesitate to ask in the forum or PM me.