My uncle Gilbert was not only a marathoner but also a climber, and I suppose it is from him that I must have learnt the verb to abseil (OED: “to descend a rock face or other near-vertical surface using a rope fixed at a higher point and coiled round the body or passed through a descendeur, the speed of descent being controlled by the rope's friction. Also with down and in extended use. Cf. rappel.)
He pronounced it ˈæbseɪl; so do I, and so do most of the people I have heard use the term. It stopped being a mountaineers’ technical term and entered general usage when people started abseiling not only down mountains but also down the outside of buildings, for charity, for fun, or in protest.
The etymology of the word is straightforwardly German: the neuter noun Seil means ‘rope’ or ‘cable’, and its derivative abseilen means ‘to lower (something, or oneself) on a rope’, hence ‘to abseil (down)’, and also, figuratively, ‘to skedaddle’. No doubt it was borrowed into English by the early pioneers of mountain climbing in the Swiss Alps.
The German pronunciation is zail, ˈapzailən (though neither of my two German pronunciation dictionaries includes the verb). The German spelling ei regularly corresponds to the sound ai (or however you choose to write this diphthong).
So why, despite this, does our prevailing pronunciation have eɪ? It could easily be accounted for as a spelling pronunciation — compare eight, rein, veil, vein etc. On the other hand in native English words the spelling ei can correspond not only to eɪ but also to aɪ (eider, height, kaleidoscope) and iː (ceiling, deceive, Keith, seize). As we all know, either and neither can go either way.
All other German loanwords with ei, as far as I can see, have English aɪ, as Eiger, eigenvalue, Einstein, Freiburg, Geiger, gneiss, Holbein, Leipzig, Weimar, Zeiss, zeitgeist. What is special about abseil?
I think the explanation must be contamination from sail, even though abseiling has nothing to do with sails.
According to LDOCE, abseil is BrE only, the AmE equivalent being rappel ræˈpel, rə-. The OED, on the other hand, defines the two terms slightly differently, rappelling involving a doubled rope but abseiling just ‘a rope’.
Both my pictures (found on the web) are captioned as abseiling. One has one rope, one has two.
As an afternote: on the melodeon discussion forum there is currently some speculation about the origin of the model name Double Ray for certain Hohner melodeons from the 1930’s onwards. One plausible suggestion is that it is from the German doppelreihig ‘double-rowed’, since these melodeons had two rows of treble buttons at a time when most had only one. This model was commissioned by a Scottish accordion dealer from Hohner, which is a German company. If true, this would be another case of German ei ai being mapped onto English eɪ.