I would guess that both report layouts are based on the same table occurrence. (The have exactly the same name selected in "Show Records From" in Layout Setup...)
If so, both layouts share the same found set, sort order and current record. Since sub summary layout parts are not visible unless their break (Sorted by) field is part of the sort order, it is very likely that the sort orders for your two different reports do not include the fields needed in order for the other report's sub summary parts to be visible.
And if you are performing a find to pull up the records needed for each report, the very found set itself may not be the same.
The simplest solution is to simply accept this as how things work and be sure to redo the find and sort when returning to the previous report layout.
Two other options:
Open each report in its own window. Then the found sets in each window will be independent of each other.
Redesign one report layout to refer to a different table occurrence of the same data source table. This requires updating each and every field on your layout to refer to the new table occurrence and also requires updating the "sorted by" fields in the sub summary layout parts.
Yes, that was the problem. Ive decided to take your advice and created a script to redo the sort on layout enter for each of the layouts.