The membrane has metal "tracks" formed on a plastic layer. Over time, where the "tails" (that connect to the QL board) are bent, this causes stress fractures in the plastic which cause small breaks (cracks) in the metal "tracks". The same happens with ZX81, ZX Spectrum (rubber key), ZX Spectrum+ and ZX Spectrum+ 128k membranes.
The only long term cure is a new membrane
Despite what people think, lead based solder IS legal in the UK. You can still buy it. The EU restriction is related to consumer electronics, Because a lot of this is ending up in land fill sites or being sent for "reprocessing" in countries where the poor use dangerous techniques to recover precious metals etc.
For use on retro computers, only use 60/40 22SWG 0.7mm solder with internal flux. Lead free solder will not work properly on components or circuit boards made using lead based solder.
Only use a good quality soldering iron and bit. 15W to 25W is okay for most jobs. Or use a proper temperature controlled iron. Keep in mind that cheap solder stations and soldering irons do not have quality control of the heat level. And China can produce really good stuff, but they also are good at producing down to a low price, but then the quality and safety suffers a lot.
When soldering, if you take longer than 2 to 3 seconds on a normal size solder pad, you are doing something wrong. You apply the wetted /tinned bit to both the pad and the component wire at the same time, then apply the solder to the joint, NOT to the iron. Allow the solder to flow then remove the iron. You can practice on some strip board by using some thin solid core wire (scrap telephone or cat5 network cable for example).
Happy computing
Mark

Standby alert

“There are four lights!”
Step up to red alert. Sir, are you absolutely sure? It does mean changing the bulb

Looking forward to summer in Somerset later in the year
QL, Falcon, Atari 520STFM, Atari 1040STE, more PC's than I care to count and an assortment of 8 bit micros (Sinclair and Acorn)(nearly forgot the Psion's)