Oh are you allowed to Short/Long Rest and maintain Concentration? It's part of Spellcasting and is considered taxing mentally, so our games rule no benefits from rests if you are maintaining a spell.
As per the PHB, page 203, your concentration on a spell ends only if you cast another spell that requires concentration, you fail a concentration check upon taking damage, or you are incapacitated or killed. The only action during a rest that would require breaking your concentration would be sleeping, which you only need to do during a long rest. Short rests (and long rests if you're a race that doesn't need to sleep) would not break your concentration.
If you use house rules to depower specific abilities, you shouldn't be surprised that those abilities are not functioning optimally.
Without house rules made to nerf it,
Hex is a perfectly viable and very powerful tool in the Warlock's arsenal. 1d6 per hit may not sound like much at first, but the ability to keep it active all day long for almost no cost (past level 5, just wake up an hour early, cast it, and short rest before you head out) allows you to add some serious damage output to your arsenal. Used in concert with
Eldritch Blast, it'll increase your damage by over a third over the course of the day. The debuff on ability checks is just gravy, and allows for plenty of creative uses. The only time you shouldn't have
Hex up is when you have an immediate need for another spell that requires concentration.
It's hard to really say how useful it might be for bladelocks, since those don't tend to be very optimal in the first place. But in that case, you should be using it similarly to the above. The only real difference being that you'll probably have more concentration-based spells to consider.