It is common for the police to keep a suspect under surveillance if they think he may be dangerous. Earlier in this thread I mentioned John Gacy. Police monitored him for about a week after their initial search of his house, which turned up evidence of foul play, but not enough to make charges stick. Eventually he got nervous and he invited the cops back into his house. This time the heat was on, so they smelled the decomposing bodies, got another search warrant, and found the victims in his crawl space.
A more recent case was the Craigslist Killer. They traced him through IP address, but he had a wireless router, so there was a small chance that somebody else might have used his account to contact the victims. Therefore they watched him until they obtained enough additional evidence to make an arrest. The police perceived this guy as highly dangerous, but they managed the risk with surveillance.