What can I do to stop hot sauce from separating?
It's normal for some separation to occur, especially based on the makeup/composition of the sauce is. 


If it's a regular long-cooked vinegar and water hot sauce, then there would be very little separation that would occur. 
If it's a vinegar and oil based hot sauce, then there would be quite a lot of separation. 
If it's a vinegar based hot sauce, but made with peppers that are very oily (habanero, hungarians, etc) and it was not made in a long-cook format, then there would be a slight separation if left unshaken for a few days. 


Remember that most hot sauces are vinegar based, with either water, juice or oil as an accompaniment, so some separation is expected, and is typically not indicative of a hot sauce gone bad.

As an example, back when I was still producing hot sauces, I had two long-cooked hot sauces (each about 4 hour simmer). One was an apple-juice and vinegar based sauce with jalapenos and lots of spices (more of a flavorful sauce than an extremely spicy sauce). The other was a vinegar and olive oil based sauce with bhut jolokia and habanero peppers. The juice and vinegar sauce suffered from nearly no separation whatsoever, as the peppers and spices were extremely well incorporated into the liquids by the long simmer time AND all the solids being ground and liquified as much as possible. The vinegar+water and oil based sauce suffered from quite a lot of separation, as the ingredients were not only not liquified, but the base by their nature tended to separate.