Your problem relays on the fact that Comcel has an issue with push notifications, when you have your phone connected to both wifi and their network, your phone prioritizes the 3G network over wifi to save energy therefore notifications depend on the mobile network not the wifi. As there is an issue with Comcel's network notifications get delayed or never arrive that's your problem and you are not alone, we all have the same problem with Comcel. When you connect only over wifi the notifications work with the wifi network and therefore your phone doesn't connect to Comcel, as a result they work perfectly.
Hey I am been having the same issue since I got my first iPhone 3 years ago with Comcel. It's been three phones a 3G, a 3Gs and a 4 and the issue unfortunately continues. I restored my phones several times in addition of taking them to Comcel's technical service with no results at all. After some research I concluded the problem has to do with Comcel because when I travel abroad the phone works flawlessly with foreign carriers and it also works perfectly when connected to wifi only. In addition to these my mom, my brother and my fiends have the same situation and they are all Comcel, not even my iPad 3G works ok with them. I have checked several sites and found that the issue has to do with Comcel's IP protocols, therefore and unfortunately for us it is a problem on their end and it seems there is no solution in the short run which means delayed notifications and most of Apple Essential services not working for us. I have contacted Comcel three times and they have only responded that their network is fine and that I am free to start legal actions against them. And so I have dicided to do exactly that, we are consumers protected by law and we are not receiving the service that was offered to us and that we are paying monthly. Therefore we are honoring the contract by paying for the services, the ones breaking the contract and the law are them. I need to get as many people to declare against them in a process in the Super Intendencia de Industria y Comercio to get them to fix the service they are supposed to supply, I am not interested in getting any monetary compensation from them I only want them to fix the issue and provide the service as they should. If you want to join please let me know, it is the only way to get them to fix the issue.