Michael,
In general, the breaking point of a given material rises proportionally to its diameter, meaning that if a string is breaking, you need to change material. This is certainly true of piano wire, and also holds for brass as I understand. There are a lot of different brass types, with different strengths, so changing alloy or process (to spring brass, if that isn't what is already there) might help. For maximum strength, phosphor bronze is an option. Reducing diameter may get you a bit less breakage, but only a small amount.
A lot of instruments are simply badly scaled - or they are scaled to a different pitch. If it was scaled to 415 (whether on purpose or not - they might have copied an older instrument), for instance, the strings might have sort of worked, but so close to breaking point that breakage would be common. I have certainly seen instruments like that. There is no magic formula beyond changing the scale (moving bridge or nut) or changing material or pitch level.
There are some scaling spreadsheets out there with harpsichord material specs embedded. I don't have such an animal myself. Maybe someone else does.