Power save mode makes it disconnect when the attached LAN device has been off for a certain amount of time. In that case, the powerline device appears disconnected as well, even though it's just sleeping. In some device implementations, this is defective however. Try a firmware update first.

What can affect powerline adapters?

Electrical noise can be a significant factor in limiting powerline network throughput. And the worst noise sources are often not obvious. Generally, motor noise from hair dryers and power tools doesn't have much detrimental effect on powerline network throughput because its frequency is too low.

Do powerline adapters lose speed?

The impact of interference is degradation of connection speeds and this is the most common issue I have seen in with Powerline. Having said that in most cases, a Powerline unit suffering from interference is still still quicker than a weak Wi-Fi signal.