SINCE the temperature WAS falling so rapidly, we couldn’t go on with the experiment.

With?

The answer is "with" If you used "since", you'd need "was" before "falling"

In this case the answer is 'With'. 'the temperature falling so rapidly' is a noun phrase, so a preposition ('With') must go before it. ('For' is also a preposition but doesn't fit with the meaning). 'Since' or 'As' (=because) are conjunctions. This means they go before a clause (=subject + main verb in a tense), which is why we can only use them if we add the main verb 'was'.

with