According to the Logistics Phase Details, section 4.2,
Axis Logistics Phase (start of Axis turn only):
Set Weather segment (22.2)
Activate Axis Armies segment (10.3)
Upgrade/Convert Ground Element Pools segment (21.1)
»» Note that though this segment only occurs during the
Axis Logistics Phase, it happens for both players.
Set Unit Withdrawals segment (18.4)
Axis Ally Surrender Check segment (19.1.4)
Soviet Logistics Phase (start of Soviet turn only):
Rename Soviet Air Group Units segment (8.1.4.3)
Award Guards Status segment (9.2)
Rename Soviet Fronts segment (7.6.6)
Rename Soviet Air HQ Units segment (8.3.2)
Disband Soviet Corps HQ Units segment (18.5.2)
Lend Lease delivery segment (21.5)
Recruit Partisan Units segment (17.1)
Partisan Air Supply segment (17.1.1)
Partisan Attack segment (17.1.2)
General Logistics Phase (for both players):
Withdraw Air Group Units segment (8.4.2)
Recover Disabled Manpower segment (18.2)
Add Admin Points segment (12.1)
Take Control of Isolated Hexes segment (15.12)
Determine if Town, City and Urban hexes are linked to the Supply Grid segment (20.1)
Upgrade Unit Fortification Level Status segment (15.3.2)
Reinforcement segment (18.1.1)
»» Reduce Unit Delays sub-segment
»» Reinforcement Arrival sub-segment (18.1.1)
Upgrade Unit TOE (OB) segment (7.2.2.1)
Ground Element segment (7.2.2.1, 21.1.9)
»» Upgrade Ground Element Types sub-segment
»» Swap Ground Element Types sub- segment
Aircraft segment (8.1.5, 21.1.9)
»» Upgrade Aircraft Types segment
»» Swap Aircraft Types segment
Production segment (21.0)
»» Add New Production sub-segment (21.1)
»» Upgrade Factories sub-segment (21.1.9)
»» Expand Factories sub-segment (21.1.8)
»» Calculate Total Rail Capacity sub-segment (21.1.11)
»» Supply Town, City and Urban hex sub-segment (21.1)
Calculate Vehicle Fuel Requirements segment (20.3.3)
Ground Element Training segment (9.3.1)
Air Group Unit Training segment (9.3.2)
Replacement segment (18.2)
»» Return damaged Ground elements sub-segment (18.2.1)
»» Return excess support squad Ground elements sub-segment (18.2.1)
»» Refit sub-segment (18.2.1)
»» Normal replacement sub-segment (18.2.1)
»» Aircraft replacement sub-segment (18.2.4)
Supply segment (20.4.2)
»» Emergency vehicle reallocation sub- segment (20.1.4.2)
»» Set Unit Supply Requirements sub-segment (20.1)
»» First supply delivery sub-segment (from HQ units) (20.4.2)
»» Automatic Rail Repair Unit movement sub-segment (14.2.1.1)
»» Emergency Rail Repair sub-segment (14.2.1.1)
»» Second supply delivery sub-segment (from Railheads) (20.4.2)
Vehicle Attrition segment (20.1.4.3)
Adjust Vehicles in Units segment (20.1.4.2)
Add Unit Fatigue segment (9.4)
Ground element attrition segment (9.5)
Reduce Fatigue and Repair Ground Elements segment (9.4.1)
Ready and Repair Aircraft segment (8.1.1, 18.2)
Aircraft attrition segment (9.5.4)
Unit withdrawal segment (18.4)
Support Unit Transfer segment (7.6.3.2)
Fortification level build segment (15.3.2)
Damaged Rail line hex repair segment (14.2.1.1)
»» Recall Construction support units sub-segment
Ground Reconnaissance segment (13.1)
Rally Routed Units segment (15.9.4.1)
Leader segment (11.0)
»» Promote Leaders sub-segment (11.4)
»» Improve Leader Ratings sub-segment (11.2.6)
»» Change Leaders sub-segment (11.4.3)
Set Unit Move Allowance segment (14.1.2)
Freeze Inactive Units segment (18.1.1)
Check Isolated Unit Surrender segment (15.12)
Change Leader Status segment (11.0)
Remove Empty Units segment
»» Combat units without any ground elements are removed from the game
This suggests that both sides' routed units check every time they can. Also,
15.9.4.1. RALLYING ROUTED UNITS
Each turn during the friendly logistics phase a routed unit will attempt to pass a range test to
its HQ in which Rnd(range to the unit’s HQ) must be less than two. If this test is passed than
the leader of the HQ unit attempts to rally the unit with a morale rating check. There is a twenty
percent chance that when an NKVD regiment (not division) rallies, it will be automatically
disbanded. There is also a twenty percent chance that Soviet tank divisions that rally will either
be disbanded and returned as a reinforcement Soviet tank brigade per section 18.1.1.1 (if prior
to September 41) or immediately converted to a tank brigade (starting from September 1941
until the end of 1941).