Advantages of Non-promotion:
You can buy 5* players cheap on the market before new season
You can save money and tokens for transfers since you will have an extra season in the same level
You can save up reds/blue/green boosters as you will not need to use those if you decide non-promotion
Also another 28 days for your players to gain skills in training
Your players do not lose a star at end season with staying in the same league
More time to develop stadium upgrades
Better chance of winning league following season
Ideal for anyone deciding to take a break or away from the game by going on holiday/vacation.
Disadvantages of Non-Promotion:
No Champions League to play in next season
Another 28 days at the same level which can become boring for some managers
No prize money in league for 8th - 14th I believe... correct me if I'm wrong
Conclusion:
If your not likely to place between 1st - 4th in your league in the current season, then its best not to finish 5th - 7th place and avoid winning promotion.