Your initial question was not clear at all. It isn't until this post that we even knew it was IMAP and not POP. To have "difficulty receiving/syncing email" wasn't clear either. What did "difficulty" mean, for example? Were receiving and syncing one problem, or two problems?
Anyway, so the problem is that you receive messages on your computer, but sometimes not on your iPhone or iPad. That's still not completely clear. When you DO receive messages on your iPhone do you always receive the same message on your iPad? Or is it random, where you receive on one or the other, but not on both? Do you ever receive messages on an iOS device that you do not receive on your computer?
Note that messages do not sync BETWEEN devices. Messages sync between the server and each device separately. So if you receive a message on one device, you must also receive it from the server on each other device. If you delete a message on one device, it is deleted from the server, and the next time your other devices sync with the server that message will be deleted on each of the other devices. You need an Internet connection from each device to receive messages on it. I know that sounds obvious, but if your iPad is a WiFi only model its WiFi is off when it is asleep to preserve battery life. Likewise if you have cellular data turned off for mail on your iPhone or your cellular-enabled iPad. In either case, unless you have Cellular Data enabled both for the device and the Mail app you only have an Internet connection for mail when the screen is lit.
Then there is when your iOS devices sync with the server. For TWC, which does not support PUSH, the options are Manual, meaning it only downloads messages when you open the mail app, or Fetch, where you specify a time schedule for downloading messages like every 15 or 30 minutes. With Fetch the email app asks the server if there is any new mail on the schedule you chose. For this to work you must have Background App Refresh enabled for the mail app. It is enabled by default, but you can turn it off.
So first check the settings I have mentioned. If they are all OK and you still have a problem, post back. One of the volunteer users here can suggest some other ideas.