Does anyone know why 上去 shàngqù gets the fourth tone in the end but 下去 xiàqu is neutral?

It does not make sense to me, since both 上 an 下 is 4th on their own. Why the difference?

I just did a quick search in dictionaries and other sites and most of them write xiàqù. In some resources looks a bit like xiàqù means the verb "to go down" and xiàqu is a complement to a verb (like 说下去). In Yellow Bridge it says, that both is possible, but xìàqù is preferred in Taiwan...
http://www.yellowbridge.com/chinese/wordsearch.php?searchMode=C&word=下去&search=Search
I'm also interested if someone can shed some light on this matter.

In Skritter, we have neutral tone for both of them as the main tone on 去, which is being used as a directional complement here.

http://comet.cls.yale.edu/mandarin/content/directional/grammar/direction-1b.htm

According to this page, you would normally use neutral tones on directional complements for 去 and 来 (except with 到 ). But that's probably a mainland thing, where Taiwan would use the full tone in this case.

Another page on directional complements, which doesn't mention tone explicitly, but does use the full tones on them:
http://www.ctcfl.ox.ac.uk/Grammar%20exercises/DC.htm

In the Skritter database, we tend to indicate them as neutral tones, but also allow the full tones. Meaning: if you answer fourth tone for 去 in 上去, it will accept it, but it still displays as a neutral tone in the prompt. That's for tone practice--I haven't fixed it so that reading practice will allow the full tone yet.

Aah. Make sense. Thanks!

Why do you think does MDBG have the Taiwan full tone for the one and the mainland neutral for the other?

MDBG is not super reliable. I wouldn't be surprised by inconsistencies.