Blue activates a Red system 3 hexes away from any of his ships.

Blue plays flank speed.

Red plays sabotage.

What happens to the Command Counter in the activated system? Does it keep the Red system activated, and hence Blue loses that turn?

Pretty much, yes. There's no limit to the number of systems you can randomly activate. This can be useful if you need to stall for any reason, and don't mind wasting command counters.

Sabotaged Flank Speeds can really suck, though, because unless you have counters to burn, a wasted action like that can hurt