sensor - How do I extend the output (high) time of my circuit (retriggerable)?

I need help with the design of a timer delay circuit for the output of a sensor circuit which can keep the output HIGH for an adjustable time range (about 1 to 10 min), after the digital output of the sensor circuit goes LOW. Also, the timer should be restarted automatically if the output of the sensor circuit goes HIGH again in the middle of the timer operation.

I saw many different power off delay timer circuits which used the 555 IC, for example, this circuit, but I can't find a resettable timer circuit.

More details: in my case the sensor circuit is a temperature circuit with a LM35 sensor and after it triggered on adjusted temperature, the output went HIGH (12V) and if the temperature suddenly drops below the trigger point, the output will go LOW as well(it contains hysteresis). I need a time delay after the output of the temperature circuit in order to keep the output HIGH for the adjusted time range, and, if the output of the sensor circuit goes HIGH again, the timer interval's must be restarted and it must wait until the signal goes LOW again(like in the motion sensors's delay circuit which id active while it's sensing motion)

-I know it is easy to do it with a microcontroller but I still need to learn more programming .
-It's not possible for me to learn programming at the moment ,so maybe a retriggerable monostable is what I want ?

Below is diagram of the temp. sensor:

^{simulate this circuit – Schematic created using CircuitLab}

schematic according to RoyC answer:

^{simulate this circuit}

Answer

To use a 7555 here you have to deal with two problems, first you have a high going control signal and second how do you retrigger the 555.

The first is fairly easy you use a simple transistor inverter to invert the input signal.

The second takes a little more understanding of how the 555 is working. It charges up the timing capacitor until it reaches a threshold voltage and then turns off. You can retrigger it by discharging the capacitor.

Look at this circuit.

Q1 and R1 invert the incoming signal to make trigger active low Q2 discharges the capacitor while the input is high giving you the retrigger function. Note with this circuit your timing period is from the input signal going low.