We present an analysis of the highly variable accreting X-ray pulsar 3A 1954+319 using 2005-2009 monitoring data obtained with INTEGRAL and Swift. This considerably extends the pulse period history and covers flaring episodes in 2005 and 2008. In 2006 the source was identified as one of only a few known symbiotic X-ray binaries (SyXBs), i.e., systems composed of a neutron star accreting from the inhomogeneous medium around an M-giant star. The extremely long pulse period of 5.3 hr is directly visible in the 2008 INTEGRAL-ISGRI outburst light curve. The pulse profile is double peaked and generally not significantly energy dependent although there is an indication of possible softening during the main pulse. During the outburst a strong spin-up of -1.8 10^(-4) hr hr^(-1) occurred. Between 2005 and 2008 a long-term spin-down trend of 2.1 10^-5 hr hr^(-1) was observed for the first time for this source. The 3-80 keV pulse peak spectrum of 3A 1954+319 during the 2008 flare could be well described by a thermal Comptonization model. We interpret the results within the framework of a recently developed quasi-spherical accretion model for SyXBs.