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I made the attached circuit to make an automatic soap dispenser ... it works well except that sometimes when the timed out ends and you take your hand from under the IR sensor the timed out is reactivated ...
You can short out C5 completely and then remove D1 and R3, they are only there to protect the trigger input from over-voltage as the TSOP output goes high. None of the measures you suggest will work properly though unless you place a much larger capacitor across the TSOP output, the drawback is it will also make it far less responsive when you do want it to trigger and you would have to limit the discharge current into the TSOP as its output went low.
Why not use first 555 as a comparator (no timing or oscillator) and use pins 2 and 6 as input for IR sensor high/low signal. Or timer 1 with IR trigger as monostable to dispense soap and timer 2 also triggered by the IR sensor but controlling the reset pin of timer 1 or something?
Knew there was something that might be useful with two 555s: Delayed Re-Triggering. Maybe you could adapt it your set-up. There may be another circuit on that page that is useful, Interlocked Monostable Timers might not fit the bill, maybe you could think of a way to re-use the idea, 'though.