This difficult saying has been understood in various ways:-

1. Some, such as Barnes, think that this is a promise of supernatural protection to a particular people at a particular time.  Barnes thinks that this was fulfilled at the time of the fall of Jerusalem, when it has been thought that Christians suffered no serious harm.  But Kidner (commenting on Psa 121:7f) notes that

‘God’s minutest care (‘not a hair of your head will perish’) and his servants’ deepest fulfilment (‘you will win true life’, NEB) are promised in the same breath as the prospect of hounding and martyrdom (Luke 21:16f.).’

2. Bengel and Hendriksen take it to mean, “Not a hair of your head will perish outside of God’s providential purpose and timescale.”  See Mt 10:29f.

3. Others, such as Marshall, France and Bock, take it to refer to spiritual safety (it is precisely such spiritual life that is promised in Lk 21:19; cf Lk 12:4-7).

4. Still others, such as Stein, incline to the view that although individuals may perish, the church of Christ will live on.