I have to use the Elixir of Longevity before using other consumables in order to get the duration extension. However, once the Elixir of Longevity wears off (in one hour) the extension I had for my other consumables is immediately dropped, making the Elixir of Longevity effectively useless. Wasted 4 dead bodies before I discovered this.
For this exact reason, i use the other elixir that you can get with the dead bodies: the elixir of potency (it increases the buff effect of all consumables by 5% for 1 hour). For me, this is a much more effective option. I think that the elixer of longevity should not have a duration itself. It should be a one time immediate addition of duration to any active consumable. Example: if you have a dragon stew active, its duration will be increased until one of the following occurs: the dragon stew is dismissed, it is replaced by another food, or it expires.