When Forrest and Jenny were running in the field to the massive tree where they sat on a branch, Forrest was running properly and bending his legs. But, when the bullies were chasing after him on bikes down the dirt path, he wasn't bending his legs and running like he did in the field. How come?
One very reasonable explanation is that Forrest outgrew the braces. Based on their construction, this would start misaligning the knee and brace joint, making it hard to bend your legs while in the braces.
This is no different from how it's really difficult to keep child prosthetics appropriately sized at all times, given their cost to replace and how fast children grow.
Or, more boringly, maybe his braces started showing wear and tear in the joints.
We also don't know the details of Forrest's condition. Maybe his muscles are stiffer after a period of no exercise, and he had been running for a while before we see him run with Jenny; we just didn't see the initial stiffness in his legs.
All in all, there isn't any explicit proof mentioned in the movie as to why these two scenes are different, but there are plausible explanations.