In Jeff's talks, he often makes specific mention of synapses grouped together as being "coincidence detectors", and he's said that it only takes between 8-20 of them, spaced 20 microns (<-- That is from memory so may be inaccurate. "Close proximity" is what we're concerned with though). If you're looking for the direct causal reason why synapses get removed, I have never seen among the papers Numenta has released, any discussion of the chemical; behavioral; or biological causes of a synapse being removed..., so I don't know.
Anyway, you may find these references useful:
As excerpted from the (Hawkins, Ahmad) paper: "Why Neurons Have Thousands of Synapses,...":
Active dendrites suggest a different view of the neuron, where neurons recognize many independent unique patterns (Poirazi et al., 2003; Polsky et al., 2004; Larkum and Nevian, 2008). Experimental results show that the coincident activation of 8–20 synapses in close spatial proximity on a dendrite will combine in a non-linear fashion and cause an NMDA dendritic spike (Larkum et al., 1999; Schiller et al., 2000; Schiller and Schiller, 2001; Major et al., 2013). Thus, a small set of neighboring synapses acts as a pattern detector. It follows that the thousands of synapses on a cell's dendrites act as a set of independent pattern detectors. The detection of any of these patterns causes an NMDA spike and subsequent depolarization at the soma.
You could try some of the references in this paper to see if there's any mention of the measurement of "longevity" of particular synapses, which is what I'm guessing you're interested in?
I've always considered the term "Permanence" to be a Numenta-born term which relates the concept of synaptic adhesion strength to a parameter which models that adhesion in code modeling. In which case, (I believe) the parameter is 2-fold: 1.) Expressing both the "strength of adhesion/degree of 'coupled-ness'" together with, 2.) the threshold beyond which a series of NMDA-Spikes are generated which depolarizes the post-synaptic cell.