The best conductive epoxy is loaded with silver. I did some experiments on it some time ago for Westinghouse. It is actually quite a good conductor up to a point. At high currents the epoxy does something weird - it goes open circuit. I never figured out why, I just know it happens. We went to welding for our high temperature and ruggedized connections. It has to get hot to do that though. But using it on an emitter that is going to run warm and then putting a good bit of current through a smallish conductor is a recipe for heating.
Solder is brittle and is not intended to carry a load. If your joints are breaking it is because of one of several reasons;
1) You are not getting wetting. Wetting is when the solder bonds to the substrate (with or copper) you are soldering to.
2) The joints are subject to vibration tending to pull them apart. No solder joint will last long under those conditions.
3) The solder joint has not been cleaned of flux. Flux will tend to damage the connection after awhile.
Of the three, 1 and 2 are most likely and are typical amateur solderer problems. 3 takes a while and is most notable on conductors like stranded wire. The wire will break right where it enters the stripped back insulation.
Clean surfaces, a good iron, good solder (lead/tin is still the easiest to work with) either fluxed or using a good flux are essential. Flux remover chemicals are available, but good old denatured alcohol from Home Depot will work along with cotton swabs.
Practice until your joints are nice and shiny, smoothly filling the joint between conductors with solder, and make a good bond with no gaps, pits, or inclusions. there are lots of web sites showing you how to solder and what a good joint looks like.
Don't buy a junker $5 iron either.
This site has some reasonable information. Even their "good" joints are pretty amateurish, but they will do the job;
http://www.bestinc.org/docs/Survival_Guide/education_resources/sasoldering.html
NASA used to have good videos, but I'm not finding them. No doubt a more thorough search would find them.
I was taught to solder many years ago to military weapons specifications and still keep those standards at my current job as an engineer - I find there is no such thing as too good a joint!

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