How many times can an IC be desoldered and resoldered?
The rule of thumb is 'assume a chip you've desoldered from a board is damaged, until you've proved otherwise'. In other words, don't solder an SMD IC down to test it.

There's a significant difference between automated SMD soldering, in a temperature controlled oven with a calibrated warm-up and cool-down profile, and eye-balling the melting of solder with a hot-air gun. With the latter, it's so easy to get it a few 10s of degrees too hot, or dwell there for a few seconds too long.

The junctions made in an IC, often by thermal diffusion, can also be unmade by over-diffusion. The damage an IC gets from over-temperature is cummulative. The amount of damage an IC gets is also exponentially related to the temperature. It's impossible to give you a figure for how many times you can heat it to above its (often recommended) 150C limit, without being very precise about the temperature.

Whether it 'works' is a poor indicator of how much damage you've done after one solder/desolder cycle. If you instead measure the input leakage current, power supply quiescent current, noise level, gains before and after the thermal abuse, then you'll have an idea of how much shift in parameters that cycle caused, and how many more cycles it can tolerate before the parameter shifts amount to 'not working'.