I stayed for 10 days in Tromso over the 2016/2017 New Year - and got 3 nights of Aurora, although one was quite cloudy. The weather as Rick mentions is just a major random factor.
We did other things as well while we were there: drove around, including to Finland; snow mobiles and dog sledding; saw the whales migrating through the fjords; experienced the polar night and of course the great NYE experience in Tromso.
That's the key to it - make sure you're going to do other things while you are there. Make a well-rounded trip.
