The cosmic ray electron spectrum exhibits a break at a energy of ∼ 1 TeV and extends without any
attenuation up to ∼ 20 TeV. Energy losses strongly constrain the time of emission of ∼ 20 TeV
electrons to ≈ 2 × 104 yr and the distance of the potential source(s) to ≈ 100 − 500 pc, depending
on the cosmic ray diffusion coefficient. This suggests that maybe a single nearby source may
dominate the multi-TeV electron spectrum. Here we show that a local source of age ≈ 105 yr, that
continuously inject electrons with a fading luminosity (on timescales of ∼ 104 yr), can naturally
explain the entire spectrum of cosmic ray electrons in the TeV domain. Despite a nearby pulsar
may easily explain the fading profile, the drop of the positron fraction above ∼ 400 − 500 GeV,
make such scenario problematic. Supernova remnants accelerate mostly electrons, rather than
positrons, but they can hardly provide a fading injection. A third class of potential are stellar
wind shocks, which however are likely to have a constant luminosity on timescales >> 10 kyr and
probably cannot match the time requirement of our potential source. Therefore, the identification
of the potential source(s) of multi-TeV electrons probably requires a profound revision of the
present paradigms of acceleration and escape in such objects.