Actually, it can work both ways. If Doflamingo's strings are affected by his health, it can be reasoned that they would remain at the strength he created them at. If Doflamingo creates a string while he is at 100% health, the strength would be at 100% strength. If he is reduced to 30% health, the string would still remain at 100% strength because it's already made. Then if Doffy makes a string, it'd be at 30% strength.
There isn't a lot of evidence that Doffy's strings are affected by his health, but the fact that Luffy could break out of Parasite using brute strength in a few seconds while Jozu couldn't in a moment is an indicator. We'd have to wait for a deeper explanation of his fruit if one is ever given.
I keep seeing brute strength being mentioned, if anything, I would have though it was the haki covered area that G4 provides that broke free of parasite. Which is possible as haki is just the manifestation of a persons will which I presume comes from within, just like he can still keep his thoughts and speech. he can keep his haki, which when he activated broke free of parasite. But on the note of Doffy's strength of his strings, I don't think they get any weaker in tensile strength so his strings are still at the same strength as BC but what I think gets overall weaker is how Doffy uses them, so in speed and force sort of thing.
Durability of strings is one thing and the force with which cage is moving forward is another.The former isn't their problem , real problem is the later. They can't stop it just by destroying strings, they can be reformed as long as Joker is standing so it'd be a waster of energy to make an attempt and break them. Neither Zoro nor Fujitora was trying to save their own asses by escaping cage. They're trying to protect countless people inside cage which is why they're not attempting to destroy the cage. After dropping a few meteors on Joker's cage ,Fujitora noted that the cage has gotten weak so nothing stops him from completely overpowering it with a rain of meteors.
FLAP THREAD barely did any notable damage to Luffy where as an attack from Hody which is nothing compared to Jokers attacks did significant damage even when he was protecting himself with his KOKA. Luffy hardly recovered his haki yet for everyones surprise he was able to resist one of strongest awakening attacks of Joker. Which would support the point of Jokers attack getting weaker.
Besides , they're just metallic strings so they shouldn't be impossible to snap for decent fighters in OP but they're hard to break which makes you believe that they're more than just metallic strings and Joker has something to do with them being that strong. For all we know he could be channelling his haki through his strings to make them hard to break or channel his physical strength through strings like how Zoro channels his PS through his swords. So it is completely logical to assume that his attacks has gotten weak because of his condition.
Didn't do any notable damage? They pierced him, the haki imbued strings pierced through a haki imbued Luffy and wen't into / through him which I'm sure did some damage, then on top of that he took a barage of them into a wall too, which the next image of Luffy shows he has been pierced even more whilst under the attack of parasite, but even in a wore out state I'm sure Luffy can handle a little impalement. Look at Luffy all the way back against Krieg, he was shot continuously by those poison round and he just pulled em' out and keeps going, an exception to this is when Croco-boy sticks his hook straight through him though xD. But I've gone onto a bit of a tangent here... Doffy is obviously in a weakened state and I'm sure his haki is wavering a little than when they first started too, so for them both to clash and Doffy to impale through Luffy's haki which was comparably equal earlier (although if I'm honest I think Doffy's is better), I'd say that yeah, his haki hasn't returned to full strength just yet.
OT: Doflamingo is a BEAST! Although Flap Thread was actually a disappoint for me, you see this really cool attack of a "thousand" being mentioned and pictured and the next panel just looks as though out of the thousand just a few look like they hit? Or maybe Luffy took a barrage of them until they got through his haki? I dunno but it started out awesome and then wasn't that appealing to me :/