“Can’t keep up” is caused by a lack of resources (CPU, Disk IO, Ram).
But like you said it’s usually fine till the TPS drops too much.
Best I can suggest is:
check that your render distance is reasonable (between 8-12).
use the Spark plugin/mod to diagnose the source of the TPS issues.
If you think it’s a hardware issue, contact your provider, that wouldn’t be an AMP issue.