We park our stroller and then take the train around and get off somewhere and roam around and sometimes don't come back to get it for quite a few hours. I do this with my Peg Perego (which is a 5 year old model now though and my McClaren too). But I've also since bought 2 cheap strollers as my "Disney" strollers, so that I can leave them and not worry. We go several times a year to DLR and have never had any issues with our strollers - pricey or cheap ones, not to say things don't get stolen, but it's rare - per the other Disney chat boards. And really I'd only be concerned with a top of the line stroller, and again - I see those parked all over all the time and I doubt they have any reason to worry.