Hi!
I want to start by shedding some light on a previous similar post "My headset mic is not working ", which could be worth checking out.
Your suspicion of the wire being loose or something similar is not unreasonable. There is no full tear-down of both headset cups for this particular model, but there is a guide on Jabra Evolve 75 battery replacement where they tear down the non microphone side.
You can hopefully follow that guide to open the microphone side, and check if the wires looks detached, pinched or damaged, if this is the case you can try re-solder or replace end of the cable(s).
If you cannot make out anything by eye, you can take a multimeter and take some ohm-measurements on the microphone, or the solder pads/wire-solder on the circuit board leading to the microphone to get a gist of the workings of the microphone. If you get a short circuit (~0 ohms) or a break (~infinite ohms) it is likely that the wire, or wire connection has broken or been damaged further up. Then it is up to you if you can think you can take apart the microphone housing to inspect it for cable damage; and there you may also be able to do measurements on the microphone itself skipping the cables. If the microphone is doing a good reading (typically 100 ohms up to kilo-ohm range) whereas the wires are not, the microphone is probably okay the cables are most likely broken; then you can replace and solder on new cables.
If you get bad measurements directly on the microphone, then it is likely that the microphone per se is broken.
Alternatively you may be able to source a new microphone and arm for the headset and replace it. Tho from a quick web search I did not find any replacement microphones.
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