I would strongly suspect a dull drill bit. Fiberboard is tough on drill bits, but a sharp new one (unless it's a Chinese cheapy made from carbon steel) should certainly hold up for several holes, say 25-50 easily.
A high-speed steel (HSS) drill bit will usually have "HS" or "HSS" imprinted on the shaft near where the size is stamped. If yours don't, it's time for a trip to the hardware store. Any brand-name twist drill bits will be HSS (Dewalt, Hanson, Vermont American, etc.).
But material aside, even HSS eventually dulls. If the cutting edges at the business end of the bit appear dull or rounded, that will explain your trouble and time for a new bit. A hardware store will generally sell them individually, so no need to buy a whole new set necessarily.