No more HP from levels, but there are other ways to gain HP if you invest in them
Since an E6 character stops gaining levels once they reach 6th level, they will get no more hit points from levelling up and getting new hit dice. That's simply not a thing that can happen to them any more. However, that does not mean they are stuck with their current hit point maximum for the rest of time, since they now progress by gaining new feats, and there are feats available in the system which will grant additional hit points.
In 3.5e, the feat Toughness from the core rules will grant an additional 3hp and is one of those feats that can be taken repeatedly; this is normally a terrible feat choice in standard D&D as it's a very inefficient use of the limited number of feats you get. In an E6 game where you can hypothetically gain new feats forever you might conceivably reach a point where a couple more HP are more use to you than any other feat you can find, and you can take it as many times as you like. If you have access to it, the Improved Toughness feat in Complete Warrior grants an extra hit point per hit die, which makes it twice as useful as Toughness for an E6 character (it doesn't even have Toughness as a prerequisite, but it can only be taken once).
In Pathfinder, the core Toughness was reworked so that it already improves with extra HD, but can no longer be taken multiple times. So unless there are more feats out there which improve hit points directly - I couldn't find any with a quick search but I don't rule out their existence - that puts a bit more of a limit on your possible hit point advancement.
As well as those options, any effect which improves your Constitution will also improve your HP. The E6 rules you're using might include feats which allow you to slightly improve ability scores (such as the Ability Training and Ability Advancement feats in this E6 ruleset or this pathfinder version). Besides inherent improvement, you may also find or purchase new magical items that provide better enhancements to constitution and thus further improve hit points.