A couple of things..
Depedning on the mileage on your car, I would suspect what is called the "CPS" sensor (or is it TSP) which is like a $65 part as long as you have articulated hands and fingers to get in to replace.
This sensor is a consumable part, usally shows going bad when the engine gets warms, engine cuts out, the can be restarted right away.
However, when it really goes bad (or has been replaced by a China knockoff part) then it can show the same problems you exhibit - engine won't start, won't start, then starts and runs fine.
If it was a fuel filter, then yes the engine will be hard to start, but the engine would run rough or not run well.
The 1st place I would start is to call free Roadside Assistance (when it doesn't start) and have them come out and diagnose for free rather than driving it and getting stuck somewhere.
For "cps" replacement, I think there should be a sticky.
Fuel filter change is even a easier DIY, I choose to replace the crazy MB hose clamps with standard, should also be in the stickies but make sure you get a OE (not no brand China) fuel filter for the replacement.
Keep the faith !