how long does purpura last after using q switched laser on the face? is there any way minimize the risk?

I dont think it is purpura you are referring to.
It may be PIH .
This happen to a lot on skin type 3-4-5 using KTP 532NM.
PIH by 532nm may take up to 6 months for it to go away.

I have used a q switched doing a few test spots on my arms for letingines. My spots looked horrible for about 2-3 weeks. I had a sales rep tell me that I could use the q switched for letingines in addition to tattos, but I would never use it again....it really make you look "beat up"

Be careful using this modality to remove pigmented lesions. I am a Fitz 2 or 3, and I now have many small circular areas on my arms from which my epidermal pigment has been totally removed (probably long term) as a result of spot treating with a 532 nm Q-YAG laser.

I dont use 532nm for pigmented lesions on arms, legs, neck as the risk is too high.
You may have explained to your patients regarding the possible PIH or purpura, but they will not be happy with PIH on their faces for an extended period of time.

Most Q switched laser comes with KTP 532 / 1064 ND YAG setting. I rarely use 532 KTP to treat solar lentigines or PIH. The 1064 Q switched ND YAG works much better in this scenario. I only use the 532 KTP to treat red / orange / yellow tattoo ink in my practice. I had to erase an interesting tattoo the other day Bugs Bunny with a carrot in his mouth. I got the black ink off using the 1064 ND YAG but the carrot (orange color) remains. After 3 treatments with 532 KTP the carrot is less visible but still there. The green light emitted by the 532 KTP is annoying and harmful to my eye sight so I try not to use the 532 KTP unless I really have no other options.