@disco_stu To resume a paused recording, press the Left Arrow (Last) button on your remote. The paused recording will be the last item in your history. Select it, and your recording will resume playing from where you paused it. Same goes for other paused content in your history.
If this does not work for you, check your Privacy settings... confirm that "Watch History" is set to On.
The cloud/stream excuse doesn't explain why the pause doesn't last longer on RECORDED shows.
There is a valid technical reason for this behaviour. Systems (your computer, a server on the Internet, any system) can only have a finite number of open/active network connections, the (primary) limiting factor being the number IP address/port pairs that define connection endpoints that you can have. When a recording is paused, the stream may not tie up much network bandwidth but the network connections on the back-end systems are still active and take up scarce resources on all the servers that are involved in delivering that stream to you. (You need to think about these sorts of things when designing systems "in the cloud" that serve a huge number of customers... and this is why you hear about web sites crashing under load; their designers don't understand or consider all the factors that impact scalability.)
When a stream gets paused, Ignite TV does not know when you will ever resume that stream, so it closes idle streams and makes it as easy as possible to resume them from where you left off.
Wouldn't so bad if the box remembered which RECORDED show I was watching.
Actually, it should. If you press the "back" button on your Ignite remote, you should see that recording in your History. When you select it, playback should also resume from the exact point where you had paused the recording.