Your documentation says, "The timed trial has tamper protection and isn't reset on re-installation of your app."
This is true. Reinstalling your app doesn't reset the trial.
How does LimeLM retain a memory of a prior installation of a timed trial?
It stores the trial information separately on the hard disk. See: http://wyday.com/limelm/help/trials/
Could my customers somehow be getting around the system somehow? I doubt this, but I must ask.
If you're worried about it, then use verified trials. They can't be "reset". "Unverified trials" can be reset. Again, see: http://wyday.com/limelm/help/trials/
My product is rock solid. All prior versions have sold well for many years. I have received nothing but positive comments on the recent upgrade.
That's a very big question. There are a thousand reasons why a product isn't selling. Has the number of monthly sales dropped (in a statistically significant way) since you released the new version? Have you changed anything else, other than releasing the new version? Is 30-days too long a trial for your app (is it something that is useful as a one-time use type app, or is it useful on intermittently)?