Surely if you've been pulling your weight wrt the 'reasonable amount' of additional duty that's expected, you are not obliged to accept any more 'overtime' offered?
I assume colleagues help each other out when one needs a day off for whatever reason, but has accepting all the overtime offered become a benchmark and therefore the 'norm'?
In any industry there are always those that grab all the overtime they can get, and those that, whilst still pulling their weight, are not that interested in the extra time away from family.
(See my earlier rant after a gutfull of vodka consumed at a Russian Christmas party. Spent the night on the couch after that effort
)