Broken, slack and darn right floppy head rests on BA short haul seats is a major bug bear of mine. You get it just right but as soon as you relax the headrest flops downward to the base of your neck.

On Boeings and older Airbus aircraft the head rest can be self-fixed. The headrest is strapped back to the seat and fixed with 2 metal poppers. When the poppers unpop, the headrest drops. Rotate the cushion upwards and away allowing the elastic straps to stretch. Then you can get right in there to realign the poppers and pop them back in place. You're then free to enjoy the Highlife in peace.

Sadly the newer aircraft employ a different tension mechanism and in terms of occurance, these I have found to be the very worst offenders.