Constructing a medical model: logic gates with feedback?
It sounds like you want something more along the lines of a monostable multivibrator. For example, the 74HC123. This device produces a pulse of a set length when it receives an input. 

The internal schematic for 1/2 the device (it's a dual) is shown here: 



You can see that there are internal feedback paths (the cross-coupled NAND gates) that allow it to retain states while the external RC circuit operates. 

You can treat this as a black box with this behavior: