The problem with Frigates is that, past early midgame, they simply don't punch hard enough or take hits well enough to stay relevant.
There aren't any straightforward solutions to that, other than nerfing the bigger ships even more than they've been nerfed... and frankly, I think the bigger ships should be buffed, not nerfed, at least defensively; Vanilla's capitals feel rather squishy to me.
It used to be that the major saving grace of Frigates was that in player hands, one Frigate might ace a fleet, or at least be a significant distraction. The CR mechanic got rid of that, because it was un-fun having to chase the AI's frigates down at the end of a battle and optimax players resorted to really boring, lengthy kiting techniques to use Frigates to wear down enemies, among other problems.
First solution: make Fighters cancel Frigates, by having better speed. That ends player-frigate tactics without needing to resort to CR crippling them quickly. It would also fix the same issues with the faster Destroyers that used to be capable of out-kiting fleets. But that would mean getting rid of CR as a concept, basically, and that's a sacred cow at this point.
Second solution: make Frigates grow considerably more than higher-end ships, in terms of raw damage output, toughness and speed, if used by a leveled Officer or player with Combat perks. Don't increase their weapon range, because that would allow them to kite again; just give them more ability to dish out some pain, take some hits and leave. Leave CR in to keep them from being silly in player hands.
Third solution: make Frigates even more disposable with a soft-cap on total fleet size that treats them as considerably-cheaper resources, so that players and AI fleets can just have a heck of a lot more of them. This kind of fits with the "garbage ball" fleet concept and with the feel of the Starsector universe; a capital ship should feel really big, bad and ugly, but fleets should not be composed of multiple capital ships, but should mainly be little stuff. The AI already does this a lot more than it actually should, but it'd be nice if players had to do the same. There are various ways to approach this; one of them is to simply make paying for Frigates much much cheaper per month vs. heavier stuff, another would be to use the not-yet-seen new mechanics for fleet size, etc.