It is not visible clearly with the time resolution you chose on the scope screen, but I would assume that there always is a rising edge of the signal at the trigger timepoint (towards the left of the screen). I.e. the scope triggers as you asked it to do. But the IR signal is a complex pattern, and you have done nothing in your trigger settings to ensure that you always trigger on the same edge within the signal packet.
You will need to set a hold-off time, or e.g. set a trigger that becomes active at the end of a long high pulse (with a duration close to duration of the gap between two packets). Your Rigol scope can do that nicely.
The Tek scope probably has a slower waveform update rate, which causes the scope to be ready for the next sweep just in time for the next IR packet repeat. Increasing the memory size on the Rigol has a similar effect, I assume. But the match in times is just a coincidence; it is not the "proper" way to get a stable signal displayed. A suitable trigger setting as mentioned above is the way to go.