WordNet (r) 3.0 (2006):

press on
    v 1: continue moving forward [syn: press on, push on,
         plough on]

Moby Thesaurus II by Grady Ward, 1.0:

72 Moby Thesaurus words for "press on":
   advance, bundle, bustle, chase, continue, crowd, dash, dash off,
   dash on, double-time, drive, drive on, elapse, endure, expire,
   festinate, flit, flow, flow on, fly, forge ahead, get going,
   get moving, glide, go ahead, go all out, go by, go on, go slow,
   hasten, hurry, hurry on, hurry through, hurry up, hurry-scurry,
   hustle, inch forward, lapse, last, leap, lose no time, make haste,
   make things hum, move quickly, muddle through, pass, pass by,
   plunge, post, press forward, proceed, push, push forward, push on,
   race, roll on, run, run its course, run on, run out, rush,
   rush through, scamper, scramble, scurry, scuttle, shoot ahead,
   slide, slip, spurt, step lively, tear