This may seem a bit strange, but put out some food for the cat.
We used to have a cat that was an outdoor cat (never really came inside) and we would see it maybe a couple times a year. Always put out food and it ate it. If it is coming around at night (remember cats are nocturnal?) then at least there would be some food. Just a thought, I don't want to feed into false hope though.
Also it is suppose to warm up a bit this week