Its a bad circuit, the capacitor will take out the protection diodes in
the second inverter. The issue is after the button is pushed the input to the
second invert will jump from 0V to 5V, but then decay back towards 0V
with time constant t = RC. But when the button is then released the input
of the second inverter will be forced towards -5V, and high currents will flow
into the protection diode on that input, damaging/destroying it or even
putting the chip into latch-up.
There are many safe pulse-generating circuits out there using a '555 or
monostable. (BTW if using a 555 substitute a CMOS version, much less
noisy on the supply lines).
You can also use an RC circuit and a schmitt-trigger XOR gate (not a CR circuit, note)
It is easy enough to fix the problem with the original circuit (pointed out by MarkT), see attached. How long should the output pulse be and what 555 circuits have you tried? Post links or actual schematics if you want helpful comments.
What you want is a 74LS121 this is a single shot edge triggered monostable. Being edge triggered the pulse width is totally independent of the trigger being held in any one state.
Yes, that is a problem with that 555 circuit. Quite a ways down on this page: http://www.bowdenshobbycircuits.info/page9.htm (under heading 555 timer Mono stable), the author shows how to isolate the push button from the input of the 555 with a capacitor, so that the 555 is edge-triggered and the output pulse length becomes independent of the button state.