According to Shenton's "Collectable Clocks" the company was in business from 1864 - 1903
Tran Du Ly wrote the definitive book on this company, but as I am in the UK and don't have access to that book, I found the following brief summary on the Internet at the "Clocks Are Us" website.
Elisha N. Welch was born in Chatham, Conn. in 1807, and started in clock business by operating a foundry which cast clock weights. He was a prolific businessman, and was involved in many interests in Bristol, Conn. and the surrounding communities. Elisha Welch bought out the failed J.C. Brown clock business in 1855.
Welch consolidated his various clock companies in 1864, creating the E.N. Welch Mfg. Co.. Elisha Welch died in 1887 at this home in Forrestville, Conn. His son James succeeded him as president of the E.N. Welch Manufacturing Company.
The company was reorganized in 1903 as the Sessions Clock Co., after William E. Sessions acquired most of the stock in the Welch company. They continued operation as the Sessions Clock Co. until 1968 when they ceased clock production.