The real aviation mechanics in the group should probably speak to this.
You can test the tightness of the intake manifold bolts at the cyl head. See torque table in Franklin Overhaul Manual.
You may remember 4 of them Fell Out of my engine, in January !
I was having low speed running problems on the ground, and when it finally crapped would only make 2000 rpm
at full throttle with carb heat on and mixture full rich.. otherwise it just didn't run.
There is a rubber tube which joins the "balance" tube at the front of the engine,
which joins the right and left intake manifolds together. Check that for condition,
and the clamps for tightness.
There are flange gaskets at each end of the cast intake manifold. These can be installed improperly.
The flange bolts can be checked for tightness. Unless these flanges got loose and moved, I doubt that the rubber
ring seals will go bad. You probably would have to take these junctions apart to see if the seal was bad, and then you get to put in a new one , no matter what !
At the aft end of the intake manifold, there are also seals where the cast manifold joins the tube that bend back and joins the carburetor.. these can be put in wrong also ( read franklin overhaul manual for description of how this is to be done,
I have never done it ).
Somebody with more experienced than me can comment on all that.
If you find everything nice and snug, and nothing moving around that shouldn't.. then I cant shed any light on the subject.
There are old automotive tricks, like listening for leaks with tubes, and stethoscopes, and also
squirting oil on suspected intake leaks... either of which could be life threatening with a prop involved !
Time to hire a real mechanic !
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I would inventory any running quirks and make a list of anything out of the ordinary.
Presumably this problem either just started, or has been getting worse - right ?
So list everything out of the ordinary.
Does it start easily.
Does it idle smoothly, and will it idle slow even when cold. It Should.. and if not that is a red flag.
Read your spark plugs. Top and Bottom. What do they look like. Brown, white, oily, black, clean or clogged up with deposits ?
Will it run smoothly at all speeds on the ground... idle, taxi, fast taxi, tail up FAST down the runway, and abort ?
Will it do this both Cold and Hot ? It should. Can you duplicate the problem with the wheels on the runway ?
Try it. This is no different than wheel landing, or aborting a take off.
Try mag drop at idle, ~ 1300 rpm, 1500, 1800, 2000, etc.
Make notes.
Is the carb heat working right ? It will be worthwhile to pull the prop and cowl,
so you can fully inspect all these things.
You tested the fuel system like I suggested right ?
Mag timing, and point gap/ condition ok ? Not guess so, but tested and inspected ?
In general it is very important to have EVERYTHING to do with Ignition Spot ON.. before adjusting or delving into
you Carburetor.
Except checking for clean fuel, which would be First on my list.
Do you have a Manifold Pressure Guage ?
This can be a useful diagnostic tool.
At idle and low rpm.. you should NOT see any ticking on the Manifold Pressure gauge.