Hi Carsten and sorry for the late reply. I've been very, very busy and had little spare time just recently. A combination of work, an XM V6 with a dead 4HP20 and getting my HDi ready for its annual test of roadworthiness has eaten into my time badly...
I'm pleased you found my long thread useful.
Firstly, as pointed out, DEXRON is the wrong oil for these gearboxes and it will kill it sooner or later. That you have debris in the oil is worrying and this needs to be investigated. You either have a badly worn B or E clutch or your torque converter lock-up clutch is badly worn and breaking up. What happens is the lock-up clutch in the torque converter wears and sheds friction material which begins circulating in the oil and starts to clog the filter. It can do other damage like scoring the oil pump housing and damaging the plain torque converter neck bearing. Also, as the filter clogs, the system gets starved of oil which results in a loss of hydraulic pressure and this in turns causes more clutch slip and more wear.
The falling out of (4th) gear sensation is most likely caused by one of the main drive clutches slipping due to low hydraulic pressure, either because of a clogged filter or because of a broken spring in the valve block.
Driving it hard it would remain in 3rd gear and so you'd not experience this problem as it looks confined to 4th gear.
It would also be interesting to read the gearbox ECU with a Lexia to determine why the snow and sport lights flash. I suspect it is again clutch slippage causing an out of tolerance speed differential between the input and output speed sensors. The difference in speed registered by the two sensors is primarily how the ECU 'knows' what gear the gearbox is in and also if these is excessive clutch slippage.
In any case, the gearbox will have to be dismantled. Luckily it is not a big job to remove the engine from a Xantia (easier than it looks) and the gearbox itself is quite straightforward to dismantle providing you know how. Have you seen my
website? It does describe how to strip the gearbox in some detail and should help.
Also, I have just had delivered to me this evening a 4HP20 from an XM V6 that I shall be rebuilding for its owner over the next few weeks as time allows. That one has lost all drive and my work on that one, which I'll be documenting, may well help you with yours.
Spare parts are readily available in the UK. They're expensive but if you act quickly the most you may need are a set of gaskets, a reconditioned torque converter (essential) and a new filter along with 9 litres of the correct oil, Mobil/Esso LT71141. I know it is expensive but it is the only oil to use in these gearboxes and sadly there is NO substitute.
Hope that helps...