It appears to me, looking at the current EDB 2 on the Headway website, that the XLR connectors do not use release tabs on the preamp. Perhaps older models did?
Not all XLR's utilize a latch and release mechanism, some just rely on a friction fit. Sometimes, the latch release tab is on the cable connector. If that's the case, it might be possible to disassemble the cable side XLR enough to persuade it to come out. Even with a release tab, XLR's can be a tight fit. If both XLR connectors are plastic, they could be more prone to sticking. I never had issues with metal ones sticking, even if just on one side (metal to plastic) My preference for XLR's is to use the Switchcraft brand.