Question about restringing...

I have a tenor ukulele that I've had to restring for a second time now, due to an issue I think I solved (I broke 2 C strings in like 3 months), but my problem now is the A string. I had this same issue last time, hopefully someone has a tip or trick...

The stings are held in place with pegs. I tied 3 or 4 overhand knots on the end, put it in the hole, jam the peg down, but when I start to get pressure on the string, it either slips off of the peg and put of the hole, or the peg just pops out entirely.

Last time I strung it, I guess I just got lucky after 4 or 5 tries?

Am I missing something? Could the issue be that I switched to fluorocarbon strings? Like maybe they are too thin or something?