Sometimes I forget to charge mine for a few weekends, so I know I can get at least that many days out of it. I usually go with higher amperage batteries, but my stands do work fine with the cheaper ones. I can’t really vouch for how many years a battery lasts, as I haven’t really kept track of it, but I know multiple years.
Interestingly, we have a battery that we use to test all the stands when we build them. The stands aren’t loaded, so the draw is much less, but that battery could easily cycle 50 or more stands up and down a few times in between charges.
It is true though that batteries that aren’t of the deep cycle type aren’t designed to be fully discharged, but there shouldn’t be any reason why you wouldn’t get a couple years out of a regular lawn mower battery, if you charge it once in awhile.
I know of a couple guys that have battery tenders mounted right on the stand and just plug the stand in after every weekend. That works nicely.