The NH first had to electrify the mainline in 1907 to comply with NY's anti-steam ordinance. After that, they started pushing eastward, reaching New Haven (IIRC) a little before WWI (I don't have my books in front of me).
During WWI, there wasn't time to expand, plus the fact that they were controlled by the USRA (who was more likely to maintain the status quo).
After the RR was released by the USRA, the RR was in bad shape after being run into the ground by the gov't. Capital was used to restore the road.
In the rest of the 1920's, the NH expanded electrification in the NY area, with most of the available capital going to the NYW&B (which was a huge mistake). The NYW&B was the suburban RR that closed only 10-20 years after opening, I think.
Other capital expenses were used (as mentioned) to buy and maintain trolley lines throughout Conn., R.I., and Mass.
By the time the NH looked east again, they hit the Great Depression, and no way were they going to spend capital money then. The NH fell into bankruptcy in the mid-1930's, and the trustees planned electrification and a 4-track mainline to start in at least the Boston to Providence section after the Depression was over. (for proof, one only has to look at the 1936 East Foxboro overpass and note that while it has three tracks, the abutments are 4 tracks wide)
Well, after the Depression was WWII, which while increasing traffic on the RR, also cut way the heck back on steel uses, including things like catenary towers.
After the war, the RR invested in new passenger cars and diesels to replace the used up and old steam power-era equipment. By time that arrived, the RR was starting to see it's revenues drop, and by 1958, it was loosing money. After that, it was all downhill from there.