Draw 2 amps from a 75 amp hr trolling battery

Draw 2 amps from a 75 amp hr trolling battery should last 37.5 hours on paper, I think. How long will it really last? How often can one completely discharge it before ruining it?

The rule of thumb is about half that long.
Once a lead acid battery, even a deep cycle marine battery, gets over 50% discharged, it becomes increasingly difficult to re-charge.
The plates’ll degrade on you more quickly if you make a habit of discharging cmpletely, and that’ll result in you buying a replacement battery more often.

As a first order approximation, the battery should be able to supply 2 amps (continuous) for 37.5 hours. The end time is defined as 1.75 V/cell for lead acid (or 10.5 V for a “12 V” battery). But a number of other factors could make it a longer or shorter time.