The most common reason the unmarried partner visa is rejected is because people don't have SOLID proof that they've lived together for at least two full years. Which you have, so no worries there.
Other common reasons for refusals:
Self-employed income. There is a MASSIVE list of documentation required and if you leave one item off thinking it doesn't pertain to you, it's a refusal.
Long-term marriages. People who have been married for a long time but living elsewhere don't realise they need to prove they've been living together for the duration of their marriage.
Not understanding the visa requirements, full stop. And not providing the required documentation.
Basically, you have ABSOLUTELY NOTHING to worry about.