I have a comcast dvr remote control. There are times when I press the buttons on the remote control and the TV or dvr won't respond. I see the lights on the remote light up - but the TV doesn't do anything. Then, after a bit, the TV seems to 'catch up' to all of the remote control button pressing. Does anyone have any ideas? I've replaced batteries, doesn't seem to help.

Some system are slow.

Here is Canada we have Sympatico and Videotron

They are both satellite TV. I have the Sympatico and everything is fluid and fast. When I use the illico from Videotron, I get really mad because it is very slow. I click on the remote and it takes time to respond. When you change channel and stop pressing, the TV continues to scroll for a long time. That is the hardware and you cannot do nothing with it.
It can be software too!

When you try to debug something, put some good quality battery in it. Duracell or Energizer
Go in front of the system 2 feet way. Not in the bright sunlight, wait until it is dark. Then try pressing keys. If it is slow, here what you could do.

Is this a new problem or it has been like that for the very beginning?
The remote control can be old or used.
Remove dust on the receiver:P
Is there any stuff on the IR led in front of the remote control?
The remote control could have lost the programmation. A universal remote control can be programmed to any TV.
Since with your remote you can control a DVR and a TV, you can program it for you specific TV. Maybe you lost the program of your specific model and have a other model.
The one I have at home, I lost the usage of the TV power bouton on the remote due to physical usage.
I am 99% sure it is not the programmation of the remote. To program a universal remote control you have to enter specific number depending of the manufacturer

It you have 100% fresh battery and you are 2 feet away. The problem is the remote or the receiver. Call Comcast. Sometime my receiver is not align or deep in my shelves and I get bad reception.

Good luck