My rouncey was just injured and needed to be 'repaired' 3 rounds in a row..

[Garabaldi]

Seriously, what are the chances of that? 

So what determines how often an item gets damaged? Is it tied to weapon proficiency, or in the above case, my Riding skill, or is every item just as likely as every other item to be damaged at the end of a round?

[Mlekce]

everyone pays repairs at end of round,if you don't have money don't ride it.
Longer the round last more reapirs u pay,and also if your team loose there is higher chance for repair items.

[Storulven]

http://forum.meleegaming.com/beginner%27s-help-and-guides/game-mechanic-megathread!/
Might be somewhat outdated, but still..

[Grumpy_Nic]

repairs happen, sometimes it feels like you have to repair stuff all the time but then there will be days where you hardly repair anything at all

thats basically it. Well ye, if you cant afford equipment, go cheap