I don't think this is particularly complicated, actually: if you try to look at the situation without any ideological blinkers on, this boils down to "bog standard negotiation theory", specifically, strategic interests and BATNAs (Best Alternative To a Negotiated Agreement)!
The Israeli current BATNA seems to boil down to something along the lines of "we just keep on going as is". Yes, it risks losing them some hostages - but that is an accusation they have already been facing and that some of their politicians have already been defending openly with the argument that there are bigger, more important strategic goals at play. Israel insists that it would not accept any permanent cessation of hostilities.
Hamas' BATNA would appear to be centred around not wanting to weaken their position permanently for temporary concessions. In other words, they will absolutely not want to agree to anything that does, in fact, allow for Israel to continue the onslaught after a "break" and trade away leverage on their part without assurances that this will not be allowed to happen.
Neither position is irrational given each party's strategic goals and interests and preferred outcomes, actually! Note that I did not say "moral", "desirable", or anything of the sort. I said "not irrational"! Both parties may even have possible gains from continuing the status quo.
And, yes, 3rd party pressure can work to shift the balance, of course!
Take the much more harmless example of a price negotiation in a business deal: if my BATNA had been "worst case scenario: I walk away from this one - and sell to XY instead for 5% less" but then XY withdrew their offer, I may now be a lot more amenable to giving my negotiating partner an additional discount. Conversely, if I received an offer for 10% more, my stance may harden. While the stakes are incomparably higher here, the theory is not fundamentally different!
I genuinely don't think it's helpful to look at this in a simplistic, opinion driven "oh, but, if X just did Y" sort of way. Because that will just never happen. Shifting incentives and the securing of strategic interests secures deals - not wishful thinking!
... and, no, I have never tried to negotiate a political deal. I most certainly have multi-million contracts, and have walked away many times on the grounds that "no deal" was actually the better option at some point.