The phrase is not about literal 'trying' or 'patience' but expressing frustration over someone's actions. When you ask me the same question multiple times, you really try my patience.
Pro Tip 2/3
Emotional Impact
Use it to convey feelings of irritation or being close to losing one's temper. Your constant interruptions are trying my patience.
Pro Tip 3/3
Intensity
It can indicate that someone's tolerance is being pushed to its limits. She tried my patience with her excuses until I couldn't take it anymore.