From personal experience,
1. I don't use proxy, all botting done on home ip. Ip is static. If I really have to use proxy, it is to prevent mule chain ban.
2. Your proxy may be private/premium. Means used by you but could also mean be re-used by someone else previously. Ip are all recycled. Hence, time to switch when you are banned fast.
3. Bans are pretty intensive these days. Banwaves happens occasionally in f2p.