2 day competition

Suspect it depends.
Am sure I've played where the handicap is fixed for both, and also where there is an overall 2 day result but also results for each day individually (helping those who can only play one day)
 
Dec.4(a)
Alteration of handicaps in the course of a competition over more than one round In a Stroke Play or Match Play competition played over more than one round, the Committee in charge, in the Terms of the Competition, are required to establish whether or not the handicap of a player at the start of the competition applies throughout the competition. In framing the Terms of Competition played over more than one round, the following guidelines are recommended.
1. In a competition such as a 36hole or 72-hole competition played in the same day or over a number of days within a short period of time the handicap of a player applying at the beginning of a competition shall apply throughout the duration of the competition. CONGU® strongly recommends that ‘a short period of time’ be interpreted as being on the same or consecutive days and that anything else represents ‘an extended period of time’.
 
As others have said, depends on the terms set out for the competition. But I believe it's more normal, for the competition, that handicap is fixed for both rounds. But remember there will be an appropriate calculation done for handicap adjustment after each round. So you could end up point 2 up, or any amount down, when the full comp is over.
 
If the committee has decided that the day 1 handicap br carried over for day 2 that is for the purposes of the competition result only.
But the two rounds should have their own CSS calculated and be treated/reported separately for handicap purposes Clause 18.10
 
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