A search of available literature reveals very little about Thomas Shannon. I was able to find the following information:
Thomas Shannon married May 31, 1753, Ann Rand. 
There is no record of a Thomas Shannon in New Hampshire until 1726 when a "Thomas Shannon" was taxed in New Castle, this would probably have been a year or so before our Thomas' birth. It is possible that the Thomas Shannon who was taxed was the father of Thomas who married Anne Rand. As Shannon is an Irish name, and given time frame, it is highly likely that his father was one of the many new immigrants coming from the north of Ireland. These immigrants were for the most part staunch Presbyterians and were being persecuted in Ireland for not not following the Anglican faith.
Thomas and Anne were living on the cusp of an exciting and terrifying time, the American Revolution. We do not know when they died or if they lived long enough to be a witness to history in the making. I hope they did, although with three sons fighting in the war it must have been a harrowing time. As is typical of the times, little mention is made of the daughters of the family.
The date of death for both Thomas and Anne is unknown. I have seen October 1811 as a date for Anne but am not sure what the source is for that. In the 1790 census of Chester there is listed John, Thomas and William Shannon. Also on the list is Jeremiah Leavitt, the future husband of Sarah Shannon.
Parsons, Langdon B., History of the Town of Rye, NH From Its Discovery and Settlement to December 31, 1903, (Concord, NH: Rumford Print. Co., 1905), 296, digital image, Archive (http://www.archive.org : accessed 23 December 2015).
 Harriet Eliza Noyes, A Memorial of the Town of Hampstead, New Hampshire, Vol 2 (Boston: G. B. Reed, 1903) 753.
 Stearns, Ezra S., William F. Whitcher, and Edward E. Parker. Genealogical and Family History of the State of New Hampshire: A Record of the Achievements of Her People in the Making of a Commonwealth and the Founding of a Nation. New York: Lewis Pub., 1908. Print.
 Otis G. Hammond, New Hampshire Wills and Probate, Vol. 35, (The State of New Hampshire, 1936) 394.