This is an ongoing issue related to the Prime Minister's right to advise the Governor General. Mainly that he can do so with little in the way to moderate his advice. By long-held convention the Prime Minister alone has exclusive right to advise the Governor General. There isn't anything wrong with the convention per se. Conventions exist, after all, as a kind of shorthand for what 'works best most often'. They are solid but have the flexibility of not being set in stone like laws are. In this regard they are meant to compliment the laws of the land. For this reason even if Canada wanted to open the constitution to limit the Royal Prerogative I'd be against it.
So what can be done?
The problems with the fixed election date law may have an easy fix: have Parliament make it a criminal act for the Prime Minister to render certain kinds of advice to the Governor General. Since a criminal act is pretty much the quickest way to lose your seat in Parliament it would be a strong disincentive for rendering said advice. However, if some unforeseen crisis came about it wouldn't completely prevent the Prime Minister from giving the needed advice. It also wouldn't prevent the government from falling of its own accord.
But would this be constitutional?
I'm of the opinion it would be. Courts can order publication bans and non-disclosure agreements are fairly common in Canada; both of which involve limiting the transmission of certain pieces of information. We also limit fundamental rights when it serves some essential purpose (for instance, some federal officials are not allowed to vote while in office). While having Parliament pass a law which places limits on how and when a Prime Minister might advise the Governor General (or, for that matter, the Queen) would seem to violate convention it must be remembered: conventions are not laws and are not interpreted by the courts. Conventions limit activities that a strict reading of the law would say are permissible and the courts are only there to interpret actual law.
If Parliament wanted to there are several different issues this idea could be applied to (prorogation being one). If applied widely enough a Prime Minister could end up effectively neutered. The convention that the Prime Minister is the sole person allowed to advise the Governor General would be broken and a more diverse set of conventions would likely soon arise.