Most shields do not last for more than a few shots against any serious fire. They nerfed the heck out of them. The best bet is to get some regen bonuses and learn to fire a bit, duck, heal the shield, then go back at it. Unfortunately STO's ground game is not good nor fluid enough to be the sort of thing making you try to use a relatively non-existent cover mechanic... : |
In groups of players, befriend (or just be) an Engineer. They can all drop Cover-Shields, which are immensely helpful for this very reason. Stay near the shield and do what you need to, and when you take a hit or two and your shield pops, duck into cover for it to regenerate.
In an STF this is a great opportunity to use your remod as well, since even if you don't need it YET, you likely will soon.