Why does bass have more “punch” when I stand up vs. sitting?

I experienced the exact same thing.  I moved my speakers around in small increments.  I ended up increasing the distance of the speakers apart one inch and raised the front of the speakers about 1/4”.  I also had to move my chair forward about 2”.  Now the bass is close to the same standing or sitting. 

You can try the "Sumiko Method" of speaker placement, which is a bit more systematic version of what tonywinga recommends.  If you try it, you will be surprise how much a tiny movement of the speaker will change bass response.  Above all else, proper placement of the speaker or listening chair will have the greatest impact on the sound (and any improvement will be free of cost).  You can find a description by Googling the method and buying a copy of Wasserman's "Duet" (A song called something like "The Ballad of the Runaway Horse" is used to find the best speaker location; you will get sick of the song).

It does make sense to put a rug on the floor between the speaker and the listening position to kill some floor bounce, and likewise, to not put a coffee table in front of the listening position (or put stuff on the table to break up reflections), but this really does not have an impact on bass response; bass waves are not affected much by putting minor obstructions in their way.  But, one aspect of floor bounce is important--speakers are often designed to account for the wave cancellation from floor bounce, so one should be cautious about introducing big changes in height of the speaker or the listening position.

Tonywinga.  Thanks. Did you change the angle (i.e. toe in) of your speakers as well?

Yes, but only by 1/8”. 

As many have already advised, you are most likely sitting in na bass null. I had the opposite issue where I had a bass node in my seating position and it would disappear when I stood up. I used an online room mode calculator and voila, I had a vertical bass node. Suggest you try the same. Wont cost you anything. Just get your room dimensions and put them in to a room mode calculator and it will show you what's happening. In my experience, you cannot get rid of the null unless you change your seating position. Or like someone else also suggested, get 2-3 Subs around your room, which will help improve the situation.