Can’t receive emails from apps

Ok, if you have been receiving emails from these apps, and they stopped coming, there could be a number of reasons:

• Your phone was updated and the versions of apps no longer support the newest version of iOS running on your phone. In this case, you would either need to wait for updated versions or have to contact each app developer to find out when they will release an update.
• Your phone was not updated recently, but for some unknown reason the Mail app is not getting these emails.
• There is something amiss with the email account you are using to receive these emails.

At this point, I would suggest that you perform a "Force Restart" of your phone. This type of restart often resolves these types of problems. At least, it's worth a try. Ref: Force restart iPhone - Apple Support

What apps are you referring to? What exactly do you mean by you can't receive back your emails from these apps?

Ref: Writing an effective Apple Support Communities question - Apple Support Communities

Sorry, but I'm a bit confused. Are you saying that these apps would periodically send you emails? That would be new to me.

Where do you receive these emails? Within the app themselves or in the Apple Mail app? If it is the former, did you recently update your phone's iOS version? ... and which exact model is your iPhone and what version of iOS is it running now?