The phrase "to pump each session" means to put in a lot of energy and effort during each session or activity.
Sentences with «to pump each session»
Power pumping does exactly that, but you complete the extra pumping sessions in one hour each day rather than spreading them out. (breastfeeding-magazine.com)
Typically three times a day is the average number of pumping sessions for a full eight hour work day. (evenflofeeding.com)
If you can, try going a little longer in between pumping sessions like every 2 and a half hours so your body has more time to replenish the milk. (lansinoh.com)