Is our time to die predetermined?

The answer is NO, we do not have a predetermined time to die.

Rather than supporting fate, the Bible says that death is often due to 'unexpected events'.
Ecclesiastes 9:11

But doesn't the Bible say that there's 'a time to die'?

Yes Ecclesiastes 3:2 says that 'there's a time to born and a time to die; a time to plant and a time to pluck up that which is plant'.

However the context of this verse shows that the Bible is discussing the continuing circles that are common to life.
Ecclesiastes 3:1-8

God has not set our personal time to die any more than he forces a farmer to plant at a particular moment.

Instead the point is that we should avoid being so preoccupied with mundane matters that we neglect our creator.
Ecclesiastes 3:11; 12:1,13

We can live longer if we make wise decisions.
Proverbs 13:14. Deuteronomy 6:2

We can carelessly shorten our lives by bad or foolish action.
Ecclesiastes 7:17

No matter how wise or careful we are, though, we cannot escape death.
Romans 5 :12

Yet this situation will change because the Bible promise a time that " death will be no more".
Revelation 21: 4