When unit is in fleeing state it may be forced to pass Ld test for routing by following events:

• enemy hits fleeing unit with attack\spell (even if landed hit fails to wound)
• number of models in unit < 25% of its initial models number. This Ld test happens only once at the end of every melee round and before Ld test for rally 
• ...

A unit has to pass Ld tests for routing only once during every x seconds. In other words, if a unit has successfully passed Ld test for rout it will be immune to any of the previously mentioned events during the next x seconds.

If a unit fails to pass Ld tests for routing its state permanently changes to Rout for the rest of battle and unit attempts to leave battlefield by reaching its closest border.

DO testnotes

• unit may rally even when enemy unit is very close (but not hitting it with melee(overlapping) or ranged attacks)
• fleeing unharmed unit can be routed even while being far away from an enemy and without taking any single wound\loss (I guess it confirms that DO may have critical roll rule from TT, i.e. when unit rolls double 1 out of 2D6 roll)

DO manual

in Table Top rules

Routing Ld test is not present in 8th or 4-5th TT rules editions(either not present in SOTHR) and was introduced in DO.