How to determine how long a relay can stay engaged?
The air temperature around the case of the relay should not exceed the published rating. The referenced data sheets show a maximum ambient temperature of 85C or 105C for one variation. There also derating curves for operation above 40C. That information shows how the relays are intended to be used. If the relays are in a confined space or in a space that has other heat producing items, you need to test or otherwise verify the air temperature around the relay.

The relays should be ok kept operated permanently unless they are in a very confined enclosure. It is unlikely that they would overheat unless the temperature outside their enclosure is also high.