I too mainly queue solo on Republic, so I often expect to loose. Seeing as a play a medic though, I just try to heal everyone as much as possible to give them all more experience fighting people in hopes that they'll get better and we'll start winning. I enjoy it, and I try to encourage better teamwork (reminding people to respond to incs, focus healers, etc.).

I'm a beginner, but I play a decent amount of PvP because I enjoy it.