Bad Apartment Wiring?
Multiple GFI's incorrectly wired in series on the same circuit must be reset in the order they appear on the circuit.  In other words, your appliance may have tripped more than on GFCI-- its not supposed to be done that way, but it happens quite frequently.  While annoying it's not unsafe to have multiple GFCI's miswired in that manner.  

Look for other tripped GFCI's (perhaps even the bathroom) that need to be reset, then try to reset the one in the kitchen you're having a problem reseting.

Your appliance likely has a ground fault and the GFCI is protecting you from shock.  

It is possible for a GFCI to reach end of life, it's far more common tho to have multiple GFCIs miswired.