Once I joined an rp in which the GM disappeared before it had even started. In the end we decided to make a temporary thread and play with our characters there until the GM returned, and then the GM could decide if they would want us to continue in that thread or start from the beginning. Personally I think this is a completely reasonable thing to do if the GM disappears before the roleplay even starts and everyone are excited to start it. It gives the GM a say in it if they come back, but it also gives the players a way to start and get into their characters while waiting.
If the roleplay has already started when the GM disappears, then I think it's completely okay to continue if they don't return within a few weeks. Just like people should be able to continue even if one character disappears suddenly in the middle of a talk and doesn't return for a few weeks, the players should be able to continue playing even if the GM has abandoned the game. The only time I would say it's not okay is if the GM has logged in and said "I will be gone for a while because of this reason so we will put this rp on hold until I can return if everyone are still interested then." Or "I cannot continue this rp any longer and will close it."
If no information is brought to the players about the GMs whereabouts, then I see no reason for them to not keep going if they really like the game and it doesn't seem like their GM is coming back. Then if the GM comes back a few months later it's just to give them information about how the plot has moved forward, and then they can decided to get back in and take command again if they wish. Or maybe you make an agreement to jump back to where the GM disappeared because the GM wanted it to go into another direction.
Of course, one should always try to contact the GM first and see what's going on and why they're not replying any longer. This is just if they don't answer at all and doesn't log in anymore. In the end it's up to everyone in the rp to make a democratic decision, do we want to continue without the GM or do we want to stop and hope for the GM to come back? The GM is the absolute authority when it comes to their roleplay, but once they are gone, personally I believe it's up to the people in the rp to decide together what to do if the GM has given no instructions of what to do in case of their sudden disappearance.
Edit: Though if you want to be respectful and wait for the GM but also continue, you can always create a new thread for the rp and continue from where you are, but then go back to where you were when the GM disappeared. That way you don't have to fear hurting the GM's feelings by hajiking their game completely as the main thread will be as it was when they left.
