In short, it’s not impossible actually, it’s just more difficult.
The radar on the F-14 uses HPRF only and they have issues picking up targets in rear aspect. This is due to their high range ambiguity, as in they are pretty bad at measuring range accurately. To HPRF radars, essentially a lot of signals from widely different ranges seem to overlap eachother due to this high ambiguity. As a result we can only really measure targets based on their speed (ranging is done seperately through another method iirc).
Anyways, so for rear aspect (~ 0 m/s closure rate) we have an extra problem. Due to radar clutter from sidelobes (or the main lobe) we get radar returns from the stationary ground underneath you, which travels with the aircraft so to speak (you always have ground underneath you). This gives you a big fat radar return which reads ~0 m/s closure. Due to range ambiguity we can’t really discern it from your intended target, which may have a vastly different range than you have to the ground clutter. As a result any target that has similar closure speed to the ground (~0 m/s) ± a margin gets hidden inside this clutter, preventing a lock.
Now, if you fly high, where this sidelobe clutter is vastly weaker or not present at all, you can lock targets in the rear aspect, or if the target you are lockin from the rear has a very high closure rate still (or is flying away very fast).
Here are two examples that show you it’s possible to detect targets in HPRF from the rear still inside the clutter region:
Low altitude rear aspect (matching speed):
Target gets hidden inside the clutter
Spoiler
High altitude rear aspect (matching speed):
Target is able to be seen through weak clutter
Spoiler
Why “proper radars” can lock in the rear aspect is because they use MPRF or LPRF waveforms. PD (all-aspect) uses MPRF and SRC uses LPRF, these waveforms measure range more accurately, especially the latter. Though SRC has a whole other can of problems with ground clutter, due to not being able to seperate (stationary) ground returns with moving aircraft due to high velocity ambiguity. MPRF is a mix of both and fixes the problems of HPRF and LPRF, and allow for somewhat accurate velocity and range measurements, which allow them to filter out ground and sidelobe clutter, making them be able to lock in all-aspects.
The F-15 uses PD (MPRF), though it also has HPRF modes, which can not detect targets near the 0-speed region, and afaik it only has MPRF (PD) for STT anyways, so you can’t force a HPRF lock even if you tried. The search HPRF modes the F-15 gets even are so nice to already completely not even show detections with <40 m/s closure rate and <5km range.
As for the Sparrow itself losing lock, they use CW, which can be thought of as HPRF but throw out the range detection entirely, just only velocity. Which causes the same rear aspect problems, more or less.
Hope this answers your question. At least this is my understanding of the problem.