Thanks a lot many people who responded with tips and suggestions. I am
following up my post from last week, after some more investigation.

1. This particular 3-way switch has "always" misbehaved -- at least for
8 years since I bought the house.

2. The house has two other places with 3-way switches (laundry room and
another hall way). Both these places work fine.

Ironically, the functioning switches are older (38-year originals with
the house), cheap looking / simple toggle switch. The the non
functioning ones are newer looking (probably put in by previous owner),
gleaming white, wide soft press buttons (3/4 wide kind).

3. I opened up 2 working and 2-misbehaving 3-way switches -- all are
3-way switches. Below is the result of using a simple electrical tester
on all the switches. Earthing is by touching the outlet box / naked
coper wire in it. The engineer that I am, I took measurements of all
possible combinations, and mad my wife make a note in the matrix
format.

U == up; D== Down; B1= black wire 1; B2 = black wire 2;
R = red wire; 1= tester lights up; 0 tester does not light up.

Functional 3-way switch
A_U,B_U A_U,B_D A_D,B_U A_D,B_D
Side A
B1, earth 1 1 1 1
B2, earth 0 0 1 1
R, earth 1 1 0 0

Side B
B1, earth 1 0 0 1
B2, earth 0 0 1 1
R, earth 1 1 0 0

Non-functional 3-way switch
A_U,B_U A_U,B_D A_D,B_U A_D,B_D
Side A
B1, earth 1 1 1 1
B2, earth 0 1 0 0
R, earth 1 1 0 0

Side B
B1, earth 1 0 0 0
B2, earth 0 1 0 0
R, earth 1 1 0 0

Beside the 48 measurements summarized above, I also took another set of
48 measurements (B1 to B2, B2 to R; B1 to R * 4 state-of-switches * 2
set of switches). I don't think this measurement is relevant. From the
above, I concluded that something was wrong with switch B, since it was
not getting any power in many cases.

So I replaced switch B. No luck. Then I replaced switch A, also and it
all worked. Then I traced through and compared my notes, final
configuration and initial configuration.

Well, the problem was at SWITCH A! B1 & B2 were swapped in switch A. Of
course, if I had known that in the beginning, I would have saved $6 for
two new switches, and about 60 minutes of testing / note taking.

But I learned a lot. Next project: hang a ceiling fan Wish me good
luck.

Bhoot Nath