In my experience, you're asking yourself the wrong questions.
Your single biggest concerns should be:
Does this fit with my business model?
How easy is it for them to find/create something similar?
If your answers are (a) not really and (b) rather hard, then stand firm and refuse.
Basically, it's one thing to be in the business of maintaining a piece of software that others market and integrate. And it's an entirely different thing to be catering to end-customers yourself. One of the worst situations you can place yourself in, is to be competing for customers with your own resellers.
Whichever arguments they've tossed at you (typically "you'll instantly reach our full customer base") are, as I've experienced them anyway, dubious at best: if your product is really good, it doesn't matter who is hosting it. At most consider white labeling, and even then I'd suggest that you think twice about it because it'll mean you'll lose control of your brand.
If they host your software and they're big, you're going to lose much needed expertise on things you'll need further down the road, namely customer care and scaling.
As a last note, keep in mind that it's generally bad to have a single customer that generates a huge chunk of your business. If any does, it basically means they own you in every sense but name. And be wary about letting yourself get sweet-talked into signing a joint venture agreement for the same reason: resellers don't like to be in bed with their competition, and you may end up with a single large customer as a result.