If one is in doubt as to whether he has fulfilled the Mitzvah of hearing Shofar then on the first day of Rosh Hashanah he is required to rehear the blowing of the Shofar, although he is not to repeat the blessing. However if this doubt occurred regarding the blowing of the second day of Rosh Hashanah one is not required to rehear the blowing.
 As the blowing of the first day is Biblical [ibid] and hence we apply the rule of Safek Deoraisa Lechumra.
 Admur ibid; M”A 585/3; Elya Raba 585/5; M”B 585/5; Nehar Shalom 585/3; Kaf Hachaim 585/24
The reason: As Safek Brachos Lehakel. [Admur ibid]
Other opinions: Some Poskim rule that one is to repeat the blessing in such a case as by a Biblical Mitzvah the Safek blessing is ruled stringently. [Peri Chadash 589/4; Rivash 221; Kneses Hagedola 585]
 As the blowing of the second day is merely Rabbinical and hence we apply the rule Safek Derabbanan Lekula. [ibid]