It'll also depend on the difficulty of each orbit, rockets that reach higher and/or deliver payloads with more extreme orbital inclinations, experience more stress and are less likely to be reliable enough to be reused.
However, the next and last iteration of Falcon 9, Block 5, is supposed to survive much more reuses, and easier to refurbish.
[1]: https://www.reddit.com/r/spacex/comments/590wi9/i_am_elon_mu...
Personally I'd expect the main stresses on the system to be due to running the engines. I see no reason to suppose that the other stresses the cores experience in flight can't be engineered round to a similar degree of resiliency.
And they do test the engines a LOT. Each new engine is separately acceptance-fired (less than full mission, but not just a burp) in Texas, then integrated into a full stage and acceptance-fired again in Texas. Then, the stage is brought to the launch site and a very short static fire test is done. If there are any last-second aborts (i.e. after engine ignition but before clamp release), that puts another short cycle on the engine. So launch will be at least the 4th firing of each engine. And if it's the center engine, it'll do a boost-back burn, an entry burn, and a landing burn. So the engines get a lot of work done even on a nominal mission before we talk about reflying the stages.
And since each Falcon 9 takes 10 engines, that means they do (depending on the mission type) around 40-50 engine firings per launch, so yeah, over a half dozen or so launches, they ARE indeed doing hundreds of engine firings, just not all on the same engine and same booster.
A simple answer to your question. We don't know yet, and it's going to be changing for a while yet.