Just a few quick follow-up thoughts. The claim of Z's defenders is that he has authority to declare martial law, which he has done, and that this includes suspending elections as he has done, and therefore it's OK for him to remain in power. As near as I can tell the critics argue that while martial law is a defined constitutional power, it doesn't explicitly say Z can stay in power past his term, making the defenders's claims an argument from silence. In other words, this is an undefined gray area.
Seems to me this is an ugly place for a representative republic to find itself in, and constitutions should be written to avoid this situation. A ruler should not have a loophole available by which they can just declare a crisis, suspend elections and then forever after claim to still be in crisis to defer elections permanently. There should be defined limits or checks by which his attempt to maintain control can be over-ridden by, say, a supermajority in parliament/congress or supreme court or whatever.
""As near as I can tell the critics argue that while martial law is a defined constitutional power, it doesn't explicitly say Z can stay in power past his term..."<
Making up the rules to suit your needs. RATS do it all the time.