The short answer is yes, changes in the Earth's magnetic field would cause a lot of troubles. But here's a longer answer:
Currently the Earth's magnetic field does a pretty good job of diverting particles from the Sun and protecting us from solar winds. The weakening of the Earth's magnetic field would change a lot of things:
First of all solar winds reaching the Earth could knock out our computers and communication systems, it's obvious that this will effect space exploration.
Second of all humans in space would be even less protected against radiation, thus making human space exploration even more dangerous and riskier.
By the weakening of the Earth's magnetic field our satellites would be also more exposed to solar winds. If the satellites aren't well protected against solar winds, we could loose them.