The problem seems to be with the iron, so staves are OK, and magic weapons are unaffected.

Yup it's part of the storyline, the iron problem.

Getting a magic weapon will prevent it from breaking, so try get something that's +1 or has a fancy name, until then you can just carry around a spare weapon.

Luckily the chance is small, so a spare metal weapon should do. If you want to make the iron crisis seem more reasonable, use the Breakable Non-Magic Armor, Shields and Helms component of BG1 Tweaks for vanilla BG1, or the same component in BG2 Tweaks for the TUTU conversion (the BGT conversion has it by default).