Why does adding this low pass-filter to a monostable multivibrator prevent triggering?
According to this old SN74121 datasheet from TI, the low-level current sourced by the A2 pin you're driving could be as much as 1.6mA.
The maximum voltage you can apply to an Ax input on this device and still have it recognized as a LOW is 0.8V.
So, Ohms Law gives us the maximum resistance you can use as a pull-down is:
$$R = V/I $$
$$R = 0.8/1.6^{-3}$$
$$R = 500\Omega$$  

Your 100k\$\Omega\$ resistor is way, way, way too high to pull that input to a low state.
500\$\Omega\$ is a worst-case value and you've seen that 1k\$\Omega\$ works, but I wouldn't go any higher than that.  

If you can't replace the 74121 with a CMOS version like something in the HC/HCT family and you need such a large RC filter then you'll have to buffer the signal between the RC and the 74121 - a schmitt trigger (with a CMOS input) should work fine.