Gearbox when warm won't change up from 3rd

Hello, I have a 4.4 v8 L322 2003 & I tow a caravan, from a cold start there does not seem to be a problem (as I know of because we store 55 miles away from home) but if I hitch up the caravan when engine & gearbox is at normal operating temperature after a few miles the gearbox won't change up from 3rd to 4th & then to 5th.
If I go into manual (Tiptronic) the indication indicates 4th & then fifth but does not change the gearbox to 4th or 5th.
When I release gear stick the indication drops back to 3rd, I have tried stopping, swithing off & then after a minute or 2 starting off again.
It changes ok through to fifth and after a sort distance drops back to 3rd and the rev's go round to 3500 until you realise what happening and take your foot of accelertor pedal but just before this you feel a surge & drop back of speed.
Please help if you experanced this problem & how to solve it.
Regards
Arthur

sounds like a box failure there is a guy on this forum that repairs them or you can search a guy in newark not used him personaly but a few of my customers have

bemble is the name, he knows his stuff

Had a similar problem with a wagon of no pedigree (Spannish word for something very rude with a happy ending) - got lucky and a fluid change fixed it.

May be worth a go before spending lots of dosh.