Hello Mark,
Based on my research issues with a Wireless Keyboard and mouse not responding randomly could occur if one or more of the following condition are true:
- The batteries that you are using are rechargeable.
- The batteries that you are using are low in power.
- The receiver is plugged into a port that is not working.
- The wireless device that you are using has trouble synchronizing with the receiver. There may be interference from other wireless devices.
- The color of the wireless pointing device pad is preventing the wireless pointing device from suspending itself.
- There may be a connection problem in the battery compartment or on the recharge base.
To troubleshoot this issue, I would request you to try the steps provided in the article below.
If the steps provided in the link does not help, you can also try the Methods provided in the link below to troubleshoot the issue.
Troubleshoot response failures in wireless keyboard or mouse
Do let us know the status of the issue, so that we can assist you further.