First, bipolar disorder is about moods, not about salvation or theology. So try not to use that phrase if you don't have mood swings. The stigma is bad enough for these kinds of people as it is, without using it wrongly!
Second, there are several reasons I have come across why people constantly think they are not saved.
1. Bad theology. Someone close to me equates salvation with good behaviour. Since neither of us are perfect, he accuses me, and himself. He has been under pastors for 13 years who have preached eternal security. And yet, I know him, and he loves Jesus and follows him with all his heart.
2. More bad theology. Order of salvation:
a. justification Romans 5:1. God saves us, we believe and we repent.
b. sanctification Romans 12:1-2 Phil.1:6 2 Cor. 3:18- we follow Jesus the rest of our lives. We make mistakes, confess our sins, and do our best to love Jesus and our neighbour as ourselves.
c. glorification - Romans 8:30, 1 John 3:2, 1 Cor. 13:12 - when Jesus returns for us.
Anyone confused about theology would do well to read the book of Romans 10 to 20 times, and maybe read some commentaries on it.
3. Some forms of OCD like Scrupulosity. Where people think they have to do things to be saved, or they will lose their salvation. You don't sound like you have this, but I don't know you. See a doctor if you do, this is a mental illness, not spiritual. There are meds and therapy helps.
4. Of course, the obvious, the person is not saved. I don't know how that happens! If you believe and repent, you should be saved. Rebuke the darkness and send it away!
Just some ideas of mine!