First off, through testing over time i have had to edit this due to new info, so bare with me on the editing.
While at roughly 33% stamina left in the bar, i'm unable to sprint or jump anymore. I had a mountain backpack, field vest and a KA rifle. Everything weighing in at approximately 31 kg. When i tossed off my backpack i was able to sprint, and when i took the backpack on again i was able to sprint, although my character ran at sprinting speeds but was stuck in the jogging animation. After some seconds my sprint showed the proper animation (although lagging), but moving around the same speed as when you jog (so suddenly the opposite).

Had several characters try it out. All of them loses the ability to use sprint and jumps when roughly below 33% stamina. Over the course of a longer playthrough the ability to sprint came on and off, with the same glitchy motion. Might have been that i was right on the edge concerning weight that if i drank a pipsi can i was light enough to sprint again.