The tensile stress on the material is independent of the thickness that you use: it depends only on the length of the string and the pitch you are tuning to.
For a string of a given material, of a given length, it takes so many Pascals (or PSI) of tension (pulling force divided by cross-sectional area) to tune to a given note, regardless of whether the diameter is .008" or .011" or whatever.
The short life you're getting is because the material you are using as string does not stand up to the tension due to tuning and the stress of vibration, or some other aspect of the instrument, such as the string pressing against a sharp edge. (Perhaps the instrument can be modified to relieve some source of stress.)
Once the string is damaged (develops a crack), extra thickness doesn't help; the crack spreads almost instantaneously and the string snaps. It's like a balloon succumbing to a pin prick. So a thicker string might not help.
Thicker strings will put more stress on your instrument because of all the extra tension needed to get them up to pitch.
The way to go here is to fix any sources of unusual stress in the instrument, and to search for a better quality string material.
Look for product that quotes higher tension values, for the same thickness. Don't just look at the absolute pounds that a given filament can handle, but divide that by the square of the diameter. A .018" line that can take 30 pounds is stronger material than a .022" line that takes 30 pounds, obviously. How much stronger? We divide 30 by the square inches: 30 / (.018 x .018) =~ 96000 PSI and 30 / (.022 x .022) =~ 62000 PSI. The .018" line can withstand 54% more tensile stress. This stronger material is better choice unless it is also 54% (or more) heavier than the weaker one. A heavier material has to be put under more tension to get to the same pitch, which can offset (or more than offset) any strength advantage it has.
By the way, I pulled some of these numbers from a table on this web page. As you can see, there significant differences among the monofilament lines, and some of the microfilament (spun thread) lines are way stronger. The best monofilament listed ("High Seas Black Widow") requires a .016" diameter to achieve a 30 pound strength, but the Berkeley Superline does it with a .014" thick braid, and something called "Sufix HercuLine Dyneema" gets it down to only 0.009".