Should I send another synopsis?

I'd say, send it to them again, because you haven't got anything to lose, but don't get your hopes up because it sounds like they're a bit...flaky...?

As said, send it again.

As for shelving your work, one question first. You say you were rejected 20-30 times by publishers and 15 times by agents. Did you submit to both at the same time? If so, IMO that's not the wisest way to go. If you want an agent, only submit to agents. If you want to submit to publishers, which I think is a very difficult and limiting route, then only submit to publishers. Since this subject has been well discussed on AW, you may want to refer to same.

Shelve it or not, well I think that has a lot to do with the many personalized rejections you received. If they point out weakness in your work or other ways to improve same, and you agree, why not make the changes and continue to submit? If not, bear in mind that given the number of submissions you have sent out you have only tested the water.

If you have second thoughts about your manuscript it is probably best to shelve it, work on another manuscript, and revisit it in a few months.

One reason is that if you've already been rejected by a publisher that an agent would contact, that narrows down the list they have for subbing.

Also, an agent can almost always negotiate a better contract for you than you can.

3rd, you might be able to pick up an agent with your book, and then that agent suggests tweaks/revisions that make it better/more likely to land a publisher. When you've already gone to a pub. with your possibly less-than-ready version, they're not going to look at it again even if it's coming from an agent this time. You might have sold to that publisher with the agent's advice, who knows.....but now you can't find out.

Also, trunking it after only 15 agents? Many members here have sent to 100 or 200 agents that rep their genre. Unless you're a very small niche, 15 is only a drop in the bucket.

It's never enough. A novel should never be off the market for a single day, ever, for any reason. As long as there's a potential market, pulling it is a horrible idea.

And a rejection only counts if the agent or editor requests a partial or a full. Twenty to thirty is a wide range, and you should know the exact number, but even thirty rejections is just getting started.