While there are no numbers that I can find after a in-depth hard core internet search of approximately 2 minutes, I did find a mention of armies bringing along spare bowstrings. Now, I don't think this is any indication that they broke on a regular basis but they did wear out. Which is logical, we have far better materials than they had back in the 13th century. On the other hand they didn't have giant spiders so no spider silk bowstrings or other ways of creating supernaturally strong strings.
The reason I mention this is because it goes back to a point I made earlier. One reason I don't add in maintenance, cleaning kits, whetstones so that the game is more "realistic" because I don't really have a clue and even if I did I wouldn't know where to end. It makes sense now that I think about it that people would replace bowstrings every so often, but I never would have even considered it. I have no idea what else I'm missing so I just assume that the characters are competent at what they do and do not share our 21st century level of ignorance of basic maintenance and care of their gear.