I don't use drill bits anywhere near as much building aircraft (or armor) models, as I did when I was doing railway modeling, but it was not very often I break bits.
Some tips.., first, get a small chunk of bees wax, and run the bit into it before drilling, repeat once in a while during the procedure. Second, I always chuck the bit so just enough of it is exposed, to drill the depth I need (example, for a 1mm deep hole, only maybe 2mm of the bit is exposed, eliminates flexing of the bit). If the item needs a hole drilled all the way through, I start that way, then extend the bit as I go. Finally, I often start with a smaller bit, as a pilot hole, then drill the size needed.
Jim F