  Recent measurements of rotation periods ($P_\text{rot}$) in the benchmark
open clusters Praesepe (670 Myr), NGC 6811 (1 Gyr), and NGC 752 (1.4 Gyr)
demonstrate that, after converging onto a tight sequence of slowly rotating
stars in mass$-$period space, stars temporarily stop spinning down. These data
also show that the duration of this epoch of stalled spin-down increases toward
lower masses. To determine when stalled stars resume spinning down, we use data
from the $K2$ mission and the Palomar Transient Factory to measure
$P_\text{rot}$ for 58 dwarf members of the 2.7-Gyr-old cluster Ruprecht 147, 39
of which satisfy our criteria designed to remove short-period or
near-equal-mass binaries. Combined with the $Kepler$ $P_\text{rot}$ data for
the approximately coeval cluster NGC 6819 (30 stars with $M_\star > 0.85$
M$_\odot$), our new measurements more than double the number of $\approx$2.5
Gyr benchmark rotators and extend this sample down to $\approx$0.55 M$_\odot$.
The slowly rotating sequence for this joint sample appears relatively flat (22
$\pm$ 2 days) compared to sequences for younger clusters. This sequence also
intersects the $Kepler$ intermediate period gap, demonstrating that this gap
was not created by a lull in star formation. We calculate the time at which
stars resume spinning down, and find that 0.55 M$_\odot$ stars remain stalled
for at least 1.3 Gyr. To accurately age-date low-mass stars in the field,
gyrochronology formulae must be modified to account for this stalling
timescale. Empirically tuning a core$-$envelope coupling model with open
cluster data can account for most of the apparent stalling effect. However,
alternative explanations, e.g., a temporary reduction in the magnetic braking
torque, cannot yet be ruled out.
