I would think that maybe something is wrong with the glue joints.  I usually have to teach beginners to not use too much glue, but my first guess here is that you did not use enough glue, or it was not applied properly.

Make up a couple of joints, the same way that you normally do, let them dry, then try to break them.  If they break at the glue joint, you have found your main problem.

Then it is either you did not use enough glue, or maybe you Titebond was old and useless.  There is an expiration to this stuff.

Chris

PS  To dissolve my glue joints made with Titebond, I would have to soak the glue --- a lot!  I have soaked a number of planes to remove the tissue for recovering, and did not have the Titebond let go.

PSS Welcome to the SFA.

There are several possibilities:

1.  The Titebond glue might have separated somewhat, with the resins dropping to the bottom of the container.  Make sure it's mixed well.
2.  If the glue dries too much before the parts are joined, it never really makes a good bond.  Expecially on the end-grain joints, the glue will soak into the wood faster.  You can solve this by double-gluing - put some glue on the end grain, and wipe off.  This will fill the end grain and provide a glue surface to adhere to the other part.  Double-gluing is advised for the nitrocellulose glues, also.  The technique does not add much weight, but really adds strength.
3.  Wood does swell when it soaks up water, and balsa soaks up water faster than most woods.  Keep this in mind when shrinking tissue - a mist of water is OK, and even a pretty good spray, but use some caution or the wood can swell and this will loosen most glue joints.  CA glues wick into the wood enough that they are just about impervious to this, but you do have a weight penalty with CAs.
4.  Check the joints that came apart - were they a really good fit?  Slight angles when cutting can really reduce the strength of the joint.  Keep in mind that razor blades and X-acto type blades often cut at an angle.  I sand the ends of cuts when possible to get a more square joint, but you have to sand straight and square or this doesn't help at all.
5.  One of the balancing acts we all perform in this hobby is trying to get really strong structures from flimsy, light-weight balsa and a minimum amount of glue.  Both are to minimize weight, but at some point we have to decide just how light to go, and may favor a bit more weight to gain durability.  If you used Esaki tissue, it shrinks a LOT - especially across the grain, and can actually break structures if you're not careful.  I'm learning to consider where the shrink needs to be on each section of the model, and properly orient the grain to the most favorable direction.  I'd also suggest shrinking the least amount possible to get the taughtness desired - then fix in place with Krylon or non-taughtening dope.
6.  Last, but not least - if you want to use the least amount of glue, but still get a strong joint - choose the application method that best works for you.  Using Titebond, I'd thin just a bit with water, then use a toothpick to apply to only the joint area - glue outside that area doesn't do you any good.  If you have a hypodermic glue applicator, this can work well, too.  For CA glues, you can make an applicator by sticking two tiny wires close together in the end of a stick, and pick up a small drop of CA between the wires, or cut the end off the eye of a needle to do the same thing.  Then put a couple of drops of CA on a bit of wax paper, and use the applicator to make the joints.  This can cut the weight of the CA used dramatically.

Justin