Constipation is also usually linked to IBS-C; and being on benzos doesn't really help much either. Most Gaba is produced in the GI tract so benzos do affect it. I had horrible benzo belly and constipation after withdrawal, but I am healed now. For me probiotics, some coffee in the morning, magnesium, eating an apple every day and veggies with more than 4 glasses of water keeps me regular, and exercising.
Try to stick with natural methods instead of the laxatives.