How old is the rig and when has the mast last been restepped? If it has always been sagging, the forestay may have been made too long (unlikely), or the shrouds not properly tensioned. The Furlex has an option for a integral bottlescrew, which permits adjusting forestay length (after taking the drum off and sliding the bottom swivel up, see manual), but even if you have that (unlikely unless retrofitted), you should investigate the cause instead of just curing the symptoms.
It's also possible that the forestay is failing and only hanging on by a few wires which are about to let go (especially with the backstay tensioned). Did you inspect it? The furling foil can hide a lot of damage, but most often the failures occur at the fittings rather than in the middle, unless wire strands have been broken or damaged and are now being unwound inside the foil each time it turns. If the forestay is the original one from 2003, this is a probable scenario.
Lastly, and most unlikely, the hull could have been deformed or the compression post sunk into a compromised keel matrix. Easy to check for the latter - lift the sole boards and check for cracks around the compression post.
Go have a proper look at your boat and then tell us more
