A. The state of Rhode Island currently reimburses the MBTA for all operating expenses south of the RI/MA state line, and they just funded a commuter rail extension south of Providence to attract intra-RI commuters to take transit to Providence instead of driving. However, even providing incentives such as free parking, ridership at these stations has pretty drastically missed expectations [1], and the trains are scheduled to take the same time as the bus takes in rush hour traffic. The commuting situation/parking isn't bad enough in RI like Boston or New York to make the train obviously beneficial time/money wise, when you lose schedule flexibility of when you can go to/leave work.
B. The site of the proposed train station only has two passenger tracks and is located in a high speed (125 MPH or 150 MPH) zone. Starting service to the station is not as simple as just refinishing it and having trains stop there: Amtrak (which owns the tracks) would probably insist that the state of Rhode Island quad-track through the station so that its trains can pass a stopped commuter train.
C. It's difficult to get transit projects funded near state borders, because of the mindset of "we paid for it and they all go work in the other state!".
Providence is a pretty fast-growing city, so it's possible that in 5 to 10 years the traffic situation makes a much more compelling case for people to make use of transit, but additional commuter rail service there is a kind of hard sell.
[1] http://wpri.com/2015/05/18/south-county-rail-ridership-far-s...