That kind of monitoring is done all over the world. Seismometers are installed at all areas that show active volcanism. GPS is a globally available system and InSAR is provided by space agencies in Italy, Germany, Canada, Japan, Korea, Europe, and the U.S.. But satellite predictions are still far from being a real-time warning system, with days or weeks passing between measurements. Most what is done is monitoring the behaviour of a volcano to issue warnings. That way areas that lie in dangerous areas can be evacuated. But even with all the work done, there are so many factors involved in eruptions. One example of which I know is the 1980 eruption of Mt. Saint-Helen. The eruption was caused by the release of pressure due to a landslide that took away one of the flanks of the volcano. This pressure release triggered the trapped gases to violently expand (much like opening a previously shaken soda can). Mount St. Helens under constant monitoring and warnings had been issued before. But still people died. One of them was the geologist based on the volcano observation station. The whole station got overrun by a pyroclastic flow destroying everything.
Being a volcanologist is one of the most dangerous jobs in the worlds, because it is impossible to predict the exact behaviour of a volcano.
I'm blabbering on, so trying to condense it into one sentence:
The build up might be detected, but the actual moment and extend of an eruption can still very likely be a surprise.

I hope to soon write a more detailed article about the predictions possible on Hawai'i.
Keep tuned :)