Timer Protection Circuit
You can use the NE555 as RS-flip-flop, so, without using the discharge function / "timing" function. The timing can be build without using the 555.

Noting that RESET can override TRIG, which can override THRES. you could make the following circuit.



R3 and R6 have been implemented as buttons, but can easily be adapted to the type of input signal you want. Their resistor value is R={if(time&lt; T1 ,1G,if(time&gt; T2 ,1G,1))}, so it's 1 &Omega; between time T1 and T2 and 1 G&Omega; elsewhere.  

When the BUTTON signal is low, M3 stops conducting and therefore C2 isn't longer shorted to ground and starts being charged. When the charge time equals about 20 seconds, M1 will start conducting and will short TRIG of the 555 to ground. That causes the output of the 555 to be set.
OUT is tied to mosfet M2 that keeps the TRIG signal low(1).
As soon as the BUTTON signal is released, M3 shorts C2 again, and another 20 seconds are needed to turn on M1.  

When RST of the 555 is pulled low, the 555 resets.

I'm not sure what the initial state of the 555 is, therefore I added pull-up resistor R2. C3 is not required.

(1) If M2 fails taking over fast enough, you could add a small capacitor between TRIG and GND. Because TRIG is pulled low by the capacitor at start up, you'll also need to add a capacitor between RST and ground with a bigger RC time.

EDIT
Triggering M1 at its treshold voltage isn't very accurate. You can increase accuracy in timing by replacing M1 by e.g. an open-drain comparator (with voltage reference like the TLV3011/2)