Martial law lets you arrest people without trial, but it doesn’t directly allow you to just not hold an election, and you can only declare it “unless when in cases of rebellion or invasion the public safety may require it”.

I guess you could come up with some pretence then impose martial law and make it clear that anyone voting the wrong way is going to get arrested, but at that point why bother with laws at all?

If I had to put money on it, I’d guess they contest the legitimacy of the next election, and he just refuses to step down - can only be elected twice, but he’s just there as a care taker until a proper election can happen