What would it take to suspend the rule?
A vote by the rules committee. The first four members on the committee, appointed by the RNC, have already stated they want to scrap it.
http://www.politico.com/story/2016/03/republican-convention-rules-trump-cruz-221355
Rules 26-42 will be set by the Rules Committee for the 2016 Convention, which (I think) meets this month.
It is a two step process. First the rules committee drafts the rule change and passes it out of committee. Secondly, a majority of delegates must vote to approve the rule change.
What would it take to suspend the rule?
******************
First off this are only Temporary Rules for 2016. In that one week before the Convention meets a group of 112 delegates will meet to determine the rules for the 2016 convention. Those rules will be presented to the convention after coming to order and ultimately will be voted on, accepted, amended and finally agreed upon as rules for the 2016 convention. Remember Rule 40 was changed at the 2012 Convention as a way to block Rand Paul from being a candidate in nomination. Prior to that convention Rule 40 required only five states not as as changed to eight states in 2012. In either case it shouldn’t play in this convention.
There are 769 delegates remaining to be chosen prior to the convention. Trump needs 479 delegates to win and Cruz needs 732 to win. I’d say Cruz has almost zero chance to get that number and Trump has a better chance but in reality this can still go to a contested convention.
The interesting thing, if you like watching train wrecks, is that it takes a majority of seated delegates to change any rule at all. They can rewrite the rules under a simple majority and then specify either a simple majority to change the rules mid-convention, or a supermajority for any further rules changes. As was pointed out, this is CalvinBall.
Even if Trump and Cruz combined have 80% of delegates pledged to them, that does not mean the majority of delegates actually support the candidates to whom they are pledged. This is an area where Trump in particular failed to pay enough attention early on. Trump and Cruz delegates are bound to vote for those candidates for the nomination, but they are not bound to vote in their candidate's interests for any other vote. The rules could easily change in any direction.
If the two leaders really have loyal delegates, they could change the rules to permanently close nominations prior to the first ballot. Establishment-loyal delegates could also eliminate that temporary rule completely, without giving too much offense, and argue that it was a temporary rule that had only been in effect for the unique needs of the 2012 convention.
"Each candidate for nomination . . . shall demonstrate the support of a majority of the delegates from each of eight (8) or more states, severally, prior to the presentation of the name of that candidate for nomination . . . not later than one (1) hour prior to the placing of the names of candidates for nomination pursuant to this rule and the established order of business." Both readings are completely reasonable (and the interpretation is in the hands of the person chairing the convention). Is the "established order of business" voting on a nominee, or is it each round of voting on a nominee? This could be quite a fiasco.