It's all about the recharge (both formed and broken). When formed, my shields regen faster than 1% per second. Everytime we make a pass and there's not sustained fire, my shields go up about 15-20%.
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Yes, targeting of weapons with missiles is one of the biggest dangers of the build. I pack a MRP, and I have an AFM to repair it to combat module damage from missiles. However, the quick broken regen rate allows for only a small window for someone to put missiles on me. Usually I just have to withstand a single volley before my shields are back up.
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Check my video playlist. I've built a FAS since the new patch. Mine is good... but it struggles against the absolute best meta FDL's a bit. From a hybrid perspective the bi-weave isn't near as good. It also has less armor, even with the extra compartments. The hardpoint placement is better, which is nice, but defense wins battles and the Clipper has the advantage there. Bottom line... you can make a good FAS, but it won't be the best ship out there all things being equal. Here's a vid of my FAS vs. a decent FDL...
https://www.youtube.com/watch?v=xBW9mzbd7iw