Years of DIY but first attempt at cutting a 60cm wide kitchen worktop.

My 15-year-old Bosch jigsaw seems to foul up halfway through: the blade has
jumped out of its guide roller and is bending sideways. I'm using a straight
edge clamped to the top of the workpiece but below the surface the blade has
wandered enough to ruin the cut. And the jigsaw is protesting etc.

I use this as an excuse to buy a new Bosch gst100bce jigsaw. Lovely smooth
and easy cut until about halfway through; then the same thing happens - this
time with more smoke and drama, I suppose because of the higher power of the
new tool (blade is smoking hot and bent to hell before I notice).

New blades, downward-cutting, pendulum off (on the new one - the old one
doesn't have it), very slow steady and careful all times etc etc. No
problems with chipping of worktop etc: very neat on all cuts so far. No sign
of anything which would make the chipboard worktop suddenly toiugher to cut
halfway in from the front edge.

I'm not stuck for cutting the basic lengths. I can use a circular saw or a
handsaw and if necessary finish the edge with a power planer or router. But
WHY can't I do it with a jigsaw? And - more to the point - how will I be
able to cut out a 95x48cm hole for the sink if the jigsaw fails to cut
properly after 30cm?

All advice gratefully received.