its, possible. that the upstairs toilet when flushedis sucking your trap dry. strange, rare, but possible
try this. lift the seat, place paper towels across the bowl. close lid.
have your life partner flush the upstairs terlit. look, see, if the paper "pumps" up and down. if it does, it is an indication the water is being pulled out of the trap ,
if you down stairs terlit is having the trap suked dry by upstairs.
houston!!! we have a problem!!!!!!! your either not vented, or vent is blocked
and i suspect, the flapper is leaking also......miner stuff there