At-Home Stain Job not 'Sticking' to Restored Pipe

I'm looking for a bit of advice from those of you who have had success staining your own pipes and/or refurbished estate pipes.
I recently worked on an estate Medico pipe which I stained and I have encountered an unexpected problem. While doing a test smoke with PA I was simultaneously working on removing carbon from the rim of another pipe with Q tips and lemon juice. A small drop of lemon juice got on my thumb and when I touched the pipe I was smoking, there was a dark red spot on my hand and I could see a spot on the pipe where the stain had come off. Additionally, some tar leaked out of the gap where the mortise and tenon connect (the stem is not original and the tenon is one of those metal push tenons that always seem to leak something awful. For the record, I didn't choose this stem. Someone else had started this restoration project previously and I just picked up where they left off.) and the stain started coming off where it came into contact with the tar. Now the end of the shank is noticeably lighter than the rest of the pipe due to stain loss.
To stain the pipe, I mixed a powdered aniline dye (Keda Dye) with 91% isopropyl alcohol and applied several coats with a rag. After I had the color I wanted, I buffed the pipe lightly with a rag to remove the excess stain powder that remained on the surface. Then I buffed the stummel with tripoli and white diamond before applying a coat of carnauba wax. I didn't do multiple sessions of waxing, but I did spend several minutes going over the whole of the stummel multiple times in one sitting. About 7 days elapsed between staining the pipe and today's test smoke.
Does anyone know where I went wrong? Is Keda dye inferior? Should I have used a different type or percentage of alcohol or maybe just used water? Should I have tried to set the dye with heat before or after buffing? Should I have applied multiple coatings of wax over several sessions? Is it something else I haven't considered here?
Thanks in advance everyone. I'm still pretty new to pipe restoration and especially new to staining pipes, so all good advice is very welcome!

Two things:

1. How did you remove the original finish from the pipe?

2. Switch to diluting the powders with denatured alcohol and you will want to put a top coat on to set the stain, there are

Many methods to do this the most common being a shellac mix or a danish oil treatment.

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I removed the original finish by rubbing with a wire brush and then sanding. The original finish seems to have been varnished in place and no amount of alcohol or acetone would even dull the shine.
Ah! I did a quick internet search on the difference between denatured and isopropyl alcohol. I mistakenly believed that any undrinkable alcohol was denatured, but I see my error there now.
Out of curiosity, would olive oil also work to set the stain? I plan on giving either shellac or Danish oil a try, but I'm just wondering if olive oil would work since I already have some on hand. Perhaps it would darken the stain too much to consider?
Thanks! I really appreciate your response!

Olive oil doesn't "set" so the answer is "no".
Drying oils like tung or boiled linseed would work. Fairly thin shellac is the most common way of setting the stain.

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Thanks!
Which part of the process is the best time to apply shellac or an oil to set the stain? Before buffing? After buffing but before waxing?
Thanks!

Before buffing

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Thanks for all the advice and for putting up with my noobish questions! This was exactly what I needed to know!
Happy smokes all!

How 'bout some photos before and after?

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I hope you just mean before and after the restoration because that's all I have haha. I didn't take any photos before I re-stained the spots that faded.
http://imgur.com/a/qZu6K3w

Thanks, but one pipe is a quaint, and the other photos not. Did you do the carving?

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Not quite sure what you mean by that first sentence, but yes, I did the carving. I'm quite new to carving, so it's far from perfect but it wasn't supposed to be uniform anyway. I kinda like the somewhat haphazard look you see in some carved or rusticated pipes. I would like to hear your opinion too, whatever it may be.

Is removing the finish and letting the pipe color as "unfinished" an option? The results are often quite pleasing.

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It could be an option, but I'm personally not a big fan of the unfinished look. And this pipe, like most of my restoration projects, is a learning experience for me.