One possibility : The transmission has a 'cooling strategy' mode which is activated automatically by the ECU if the transmission fluid temperature is unacceptably high. In this mode, upshifts are inhibited to deliberately maintain high engine speeds and therefore oil pump speed (and hence flow through the cooler). If you have a laser IR thermometer it might be worth pointing it at the transmission sump pan next time you get this problem to see how hot the fluid is getting.

On Range Rovers (same engine & transmission) this problem is very common because the bottom eight rows of the main radiator, which provide the cooling water to the transmission oil cooler, become blocked with sediment over time and stifle the cooling flow. I'm not sure whether or not the E53 cooling setup is the same?

Phil