Hi Heather
The 3rd Somerset Light Infantry were Militia/Special Reserves, ie part-timers. Part of the agreement for enlisting was that men had to be available for 'embodiment' in the case of national emergency, ie WW1. After a few months they obviously found he was not fit enough for full-time service, and hence his discharge. It would be worthwhile searching for a WW1 medal index card, either on Ancestry or the National Archives website, as he should have been awarded a Silver War Badge when they were introduced in 1916 -
http://www.nationalarchives.gov.uk/documentsonline/medals.aspLater on in the war they lowered the physical requirements, and he may have joined either something like the Labour Corps -
http://www.1914-1918.net/labour.htm - or a home defence battalion. However if he did not go overseas he would not have been awarded medals, and his papers for this service may have been lost. If you have any addresses for him during WW1you should check the electoral rolls. They often give details of serving soldiers.
In his case 'discharged term of engagement' – often called ‘time expired’ – will mean he had completed at least 12 years service in the RHA. Any service under the age of 18 did not count, so you should look for him being discharged in 1906 or later, depending upon the age he enlisted, and also if he extended his service in the RHA reserve. Regulars could serve all 12 years in uniform, or split between time in uniform and time in the Reserves. One problem is that Reservists tend not to give that information on census and BMD certificates etc.
Findmypast are due to publish records for men discharged 1900 to 1913 ‘this month’, so it would be worth checking these when they arrive.
Ken