  Gate control of donor electrons near interfaces is a generic ingredient of
donor-based quantum computing. Here, we address the question: how is the
phonon-assisted qubit relaxation time $T_1$ affected as the electron is
shuttled between the donor and the interface? We focus on the example of the
`flip-flop qubit' [Tosi et al., arXiv:1509.08538v1], defined as a combination
of the nuclear and electronic states of a phosphorous donor in silicon,
promising fast electrical control and long dephasing times when the electron is
halfway between the donor and the interface. We theoretically describe orbital
relaxation, flip-flop relaxation, and electron spin relaxation. We estimate
that the flip-flop qubit relaxation time can be of the order of $100 \,
\mu\text{s}$, 8 orders of magnitude shorter than the value for an on-donor
electron in bulk silicon, and a few orders of magnitude shorter (longer) than
the predicted inhomogeneous dephasing time (gate times). All three relaxation
processes are boosted by (i) the nontrivial valley structure of the
electron-phonon interaction, and (ii) the different valley compositions of the
involved electronic states.
