Based on: durchlassen
A detailed look at the German preposition "durch". We'll see what it means, when to use it and we'll collect the most important prefix verbs with "durch"
durchsetzen, durchhalten, durchmachen, durcheinander, der Durchschnitt, durchdrehen
The core idea of this root was:
letting go, slacken off, relenting
And we can still see this sense in the English offspring, like last, let, lenient, latter or late.
By the way, the words relax and and release, though they would fit in here, apparently come from a different root.