Disposition constantly drops, super annoying!

It sounds like you may be relying on intimidation to raise their disposition towards you. The "Intimidate" option is a double-edged sword, and you should only use it when really appropriate, or if you have no other choice.

The different kinds of Persuasion work in different ways. If you use "Admire" to try and raise a character's disposition towards you, then your chance of success is determined largely by your Speechcraft skill, although there are some other factors that affect your chances. If you succeed, and raise the character's disposition, then the increase is a permanent one. You can also permanently raise a character's disposition towards you by bribing them. Your chance to bribe successfully also depends, to some extent, on your Speechcraft skill, but the amount that you offer as a bribe also has a significant impact on your chance of success.

The "Intimidate" option is different. You are basically trying to frighten someone into cooperating with you by threatening them. Your chance of success is heavily influenced by your overall power level as a character. If you are successful, you will temporarily raise the character's disposition towards you, but their permanent disposition towards you will actually go down. So, if you do it enough, you can get their current disposition towards you up to 100, but lower their permanent disposition towards you down to 0.

So, if you want them to like you now and in the future, either bribe them or admire them. Bribing works a lot better if your Speechcraft skill is low, but if your Speechcraft skill is high, admiring them will work often enough to get their disposition very high (although getting it to 100 may be a challenge), and it won't cost you anything.

You should use the Bribe function the most.