  We study the decay of cosmic string loops in the Abelian-Higgs model. We
confirm earlier results that loops formed by intersections of infinite strings
formed from random-field initial conditions disappear quickly, with lifetime
proportional to their initial rest-frame length $\ell_\text{init}$. We study a
population with $\ell_\text{init}$ up to $6000$ inverse mass units, and measure
the proportionality constant to be $0.14\pm0.04$, independently of the initial
lengths. We propose a new method to construct oscillating non-self intersecting
loops from initially stationary strings, and show that by contrast these loops
have lifetimes scaling approximately as $\ell_\text{init}^2$, in line with
previous works on artificially created string configurations. We show that the
oscillating strings have mean-square velocity $\bar{v}^2 \simeq 0.500 \pm
0.004$, consistent with the Nambu-Goto value of $1/2$, while the network loops
have $\bar{v}^2 \simeq 0.40 \pm 0.04$. We argue that whatever the mechanism
behind the network loop decay is, it is non-linear, can only be suppressed by
careful tuning of initial conditions, and is much stronger than gravitational
radiation. An implication is that one cannot use the Nambu-Goto model to derive
robust constraints on the tension of field theory strings. We advocate
parametrising the uncertainty as the fraction $f_\text{NG}$ of Nambu-Goto-like
loops surviving to radiate gravitationally. None of the 31 large network loops
created survived longer than 0.25 of their initial length, so one can estimate
that $f_\text{NG}<0.1$ at $95$% confidence level. If the recently reported
NANOgrav signal is due to cosmic strings, $f_\text{NG}$ must be greater than
$10^{-3}$ in order not to violate bounds from the Cosmic Microwave Background.
