This is not specific to relationship, but I think a lot of insecurities ultimately come from attachments, especially if they relate to things we cannot avoid. For example, a loved one could die, our health could fail, etc. We cannot stop these things occurring, so the best we can do is become less attached and accept that anything could happen and that perhaps they're not as bad as we might think. You can follow this thought further at this address:
Attachment: the root of insecurity and anxiety