Have a 2007 Civic Ex w/Manual 5-spd. Wiper delay function works only at max delay at engine start-up w/control set at min delay (fully clock-wise rotation). After engine rpms are up a bit (batt voltage goes up?) wiper delay goes to min delay. If rpms low and electrical load high (lights & blower motor), delay goes to max. Seems system/batt voltage related.
I would have the battery and the charging system tested. If the battery is not taking or holding a charge, the charging system may not be able to overcome that. A long slow charge from a battery charger might help, if the battery is OK but for some reason discharged. Good luck and please let us know what you find.