It might be your cable box. I have a motorola (U-Verse) and at times is is slow to respond. I can tell the box received the signal from the remote because the power light on the box flashes, but for whatever reason it takes the box a while to perform the command.
If you do need/want a new remote I can recommend the ones I've used. For years I used a URC MX-850 in my main room, and I still use it in my bedroom. For the last year I have been using a harmony 900 in my main room. Both are fantastic remotes.
You can probably find the MX-850 online for around your price range now as it is a bit older model but be aware that there are additional costs. For example, if you need rf you have to buy a separate extender (more than $100). Also, the pc programming cable that came with my 850 was a serial cable which means i had to buy a usb to serial converter as well (another $40). Overall the 850 is a little more complicated to program but offers a higher degree of macro customization then the Harmony products. If this is important to you, I would recommend some internet research on the macro capabilities of the various remotes before making a purchase.
The harmony 900 on the other hand, comes with everything you need for rf and, in my experience, the 900's rf capability works a lot better than the 850. When I had my 850 in the main room, the rf extender seemed to always get flummoxed by external rf signals causing you to have to press commands multiple times before they would register (a pain when trying to stop your player or dvr from rewinding etc.). Ever since moving it to my bedroom (further away from the other electronic gizmos in my house) the 850's rf has worked fine.
In short, if you need rf and can afford $300 then I would opt for the 900. If you don't need rf then you could also look at the Harmony One ($200). My father-in-law has that remote and it works great as well.
