my uro absolutely loves to come out and explore outside of her cage, however if I go a day or two without letting her out, she stops basking and pooping. She still eats of course, because she is very oppurtunistic, so whenever I try to just let her go for a few days without my interaction, she eats and sleeps all of the time and becomes sort of bloated after a few days, until I let her out again, and then she'll bask and in the next day or two there will be a HUGE present. She also has the strange tendancy of going in her food bowl. Always put it back where it came from I guess.
This is why it sounds strange when I hear about other people that keep their uros in a more naturalistic environment (nice big cage, a lot less outside time, etc.), because I can't get away with a few days of letting Sam do her own thing before it basically puts her into a semi hibernation. My current theory is that how you bring up a lizard has great affects on them mentally in the future. I think that if you bring up a reptile with little contact to humans, they are used to that and don't expect it, so they can go about their daily schedules uninhibited. If the reptile has grown up interacting with humans, they might be a little thrown off when they arent' allowed to come out and have a nice walk around the room. I may be completely off, but it seems to make sense with me.
also, maybe try messing with your basking spot temperatures to see if maybe a higher temp will get the uro out and basking.