If a dental filling falls out in two months should you have to pay for it?

You should expect to pay for the filling for the first placement. If you should pay for subsequent fillings on the same tooth depends on why the filling came out. If it was due to trauma, such as getting hit in the face, then yes, you probably ought to pay for the replacement. On the other hand, if it simply broke off, it may have been that the dentist was trying to be too conservative and placed a filling where a crown was really needed. In that case, the doctor ought to credit you the fee for the filling towards the fee for the crown.

If you suspect that the dentist is simply incompetent, seek a second opinion or just find a new dentist.