  The ultra-compact dipping source \object{XB 1916-053} has an orbital period
of close to 50 min and a companion star with a very low mass (less than 0.1
M$_{\odot}$). The orbital period derivative of the source was estimated to be
$1.5(3) \times 10^{-11}$ s/s through analysing the delays associated with the
dip arrival times obtained from observations spanning 25 years, from 1978 to
2002. The known orbital period derivative is extremely large and can be
explained by invoking an extreme, non-conservative mass transfer rate that is
not easily justifiable. We extended the analysed data from 1978 to 2014, by
spanning 37 years, to verify whether a larger sample of data can be fitted with
a quadratic term or a different scenario has to be considered. We obtained 27
delays associated with the dip arrival times from data covering 37 years and
used different models to fit the time delays with respect to a constant period
model.We find that the quadratic form alone does not fit the data. The data are
well fitted using a sinusoidal term plus a quadratic function or,
alternatively, with a series of sinusoidal terms that can be associated with a
modulation of the dip arrival times due to the presence of a third body that
has an elliptical orbit. We infer that for a conservative mass transfer
scenario the modulation of the delays can be explained by invoking the presence
of a third body with mass between 0.10-0.14 M$_{\odot}$, orbital period around
the X-ray binary system of close to 51 yr and an eccentricity of $0.28 \pm
0.15$. In a non-conservative mass transfer scenario we estimate that the
fraction of matter yielded by the degenerate companion star and accreted onto
the neutron star is $\beta = 0.08$, the neutron star mass is $\ge 2.2$
M$_{\odot}$, and the companion star mass is 0.028 M$_{\odot}$. (Abridged)
