Condom Breaking

This is from the male perspective.
I swear the world is against my partner and I. Being a young age (and not nearly ready for kids), we are extremely precautionary when it comes to sex. We were unfortunate enough to experience (some time ago now), a condom breaking. It freaked us out indefinitely and I agreed I wouldn't finish in sex anymore because the thought was just simply too much. We wouldn't stop having sex, we'd just get her to climax and then later I would finish myself off. I was completely fine with this because I'd rather that until we figure something rather than stress and worry if the incident were happen again and the sound of unwanted children pitter-pattering through halls. 
Time has passed and my partner told me she wanted me to finish again. What do you know? The fucking condom broke again. Of course (like last time) I still pulled out even though we were using protection and I even stopped prematurely because I was worried still, meaning I didn't even start ejaculating until I was out and it wasn't a full load. I was wondering if anyone had any insight into this at all. 
Before you ask: Yes, I do store them correctly, yes they are not even close to being ot of date, and yes I wear them correctly (I have had the luck of being properly educated with this). We also check it during sex to make sure it is okay, but it only breaks in the time that we are doing it until I finish (which is even more weird because that part is more gental than the rest). Is this just pure bad luck and probability, or is there perhaps another reason?
NB: I am most likely going to buy some lube and try that out, and so far thicker condoms are uncomfortable (unless you could recommend a brand for me - I live in Australia if that changes anything in terms of purchase). 
Also, she did shower and (I assume) wash herself out afterwards as well just in case.