When trying to chop down a whole tree with a GregTech axe (I tried both Iron and Wrought Iron) the progress counter resets at around 93% so it's impossible to break the block. Chopping a single log while holding shift does work however.

I have the same problem, and the explication given in #106 does not seem valid. Below is a screenshot of a single tree which I cannot cut down using the GregTech axe.

Maybe this bug was introduced by an GregTech update in 1.0.6?

To further advance and Help Claim

This appears to be an issue with the more recent versions of GTCE. This issue still persists in Omnifactory 1.1.0, so as a quick fix, you can manually downgrade to gregtech-1.12.2-1.8.1.399.jar, which has working axes and chainsaws (but you won't be able to play on servers).
I also submitted an issue on GTCE's bug tracker, so lets hope the GTCE devs fix it in the next version.

Actually this appears to be a conflict with nuclearcraft according to someone on the discord who tested things so you might report to nuclearcraft instead.

This does not have anything to do with nuclearcraft. I have my own pack and am experiencing the same issue. nuclearcraft is not in my pack.