I hate to rub it in but it is a well known fact (around the interwebs) that Generac's CS is terribly lacking.
You very well may be on your own with this one.

Generac/Guardian (Generac's home center line) standby units ARE designed to work with their automatic transfer switches. They talk to the genny and also have control over the battery charge and other functions.

They don't call them gener-Crap for nothing. No offense.
You don't say if your unit is NG - propane - or diesel.
You have to do some investigating on your own. It could be
anything. Overload, underload, over amp.,low oil, low oil
pressure, Out of phase, No ground, feed wire to small,
exciter voltage too high or too low, and so on. It's going into lock out for some reason. It's protecting itself.
Get your local sparky out there to check it over. Remember
you only have 90 seconds to find it. good luck

Do some careful research, and contact the head of the company. It may be better to actually find the GM's secretary's name/contact, and contact them, and ask them to forward your concerns.

I don't think the dealer did you a favor by connecting the generator to your existing transfer switch. As petey_racer said, it's designed to be used with a compatible transfer switch. Given that, I'm skeptical of the installer's claim that they've installed hundreds of generators connected like yours.

Here's my story: My generator dealer is a guy who lives and breathes generators. He installed Generac's original home generator and automatic transfer switch for me, in 2000. That generator wasn't very good, but mine lived longer than most of them, with the help of some non-official repairs. When it finally died (governor froze up), he sold me the newer model which I've found to be far, far better than the old one. He offered to save me some money by reusing the old transfer switch. Even with advice from Generac tech support, it took a couple of tries to fix a problem where the battery would drain down while the generator was running. It's fine now and has carried us through some storms. But the installation would've gone much smoother if he had replaced my old Generac transfer switch with the new version.

By the way, in order to assure myself that everything really was ok after the second repair, I ran the generator in failover mode for 2 1/2 days (it powered the loads hooked to the transfer switch, and the rest of the house ran on utility power). That might be a bit extreme, though necessary given the nature of the problem. But my point is that you never want to wait until an emergency to find out if the thing can really do its job.