Hello
I'm sure this has happened to you.
You've got three tracks ie bass/vocal/piano.
You balance them and the bass sounds too loud.
So you lower it and, oh dear oh dear, the other two get louder!
So you lower them a bit and , oh dear oh dear, the bass is too loud again.
Before you know it, you've pulled everything to the bottom of the scales
and you start all over again. I seem to have had this problem all of my recording life.
Are there any definitive answers to this problem?
Sorry if you've heard this all before!
Echo

Never happened to me.

However, if you change this to one instrument being too quiet, turn it up, then turn up all the others, yes.  I have the inverse problem.  "Louder, louder, louder - oops I'm going deaf, turn it all down!"
 
Definitive Answer.
Step 1 was to lower the bass.
Step 2 was to lower the other instruments.  Instead of this, raise the bass 1/2 way between where it was before Step 1 and now.
Rinse and Repeat.

Hi. Others will know far more than me, but I would try to use subtractive eq to carve out space for the different instruments.
The instruments and vocals are most likely competing for the same frequencies, so making them sit in "their own space" makes it easier to mix. 
If it is a dynamic performance, maybe some compression to even out some of the peaks (if necessary).
All the best. 

+1 to what Zargg said.
 
Changing EQ settings through the track can also help - the whole number isn't static beginning to end.

I just make everything louder than everything else.
 
By at least 20-40%.
 
Through my Soubdblaster audio card of course.
 
Then it all goes crash in the loudspeakah.
 
That's my SONAH.
 

Hey, is there an echo in hear?

Lol. Hell yeah! I've been there a few times, and I almost posted the same thing you did a few months back.
 
However, I learned one trick that saves me from going there anymore. It's the "matching the kick with the bass using VU meters" trick. However, you're not using a kick on that song, so it might not be relevant. But it sure helped me out. Once I get the kick and bass volume right, and those two tracks together are peaking at -12dB or so on the Master fader, those two sliders never get touched again. Then I just build my mix from there (volume-wise) based on those tracks.
 
Here's a video on the "trick":
 
http://forum.cakewalk.com/Using-VU-meters-for-low-end-levels-m3475996.aspx
 
Sorry for the LOL, bro. But I know exactly what you're going through. I laughed at myself many times when this happened. You just gotta bite the bullet and start over when your faders are all the way down at the bottom and you can't even see any meters. Proper gain staging was probably one of the most important things I've ever learned.
 
Good luck.
 
~Jeff

Have you compressed the tracks correctly

I don't know what kind of monitoring you have but once I get down to the real mixing stage (and I'm not saying I pump out major label mixes all the time) I'm moving the faders just a few decibels or even half a decibel. With bad monitoring it's easy to overdo it in order to really hear an effect.

If the bass is too loud on some notes it could be a sign you need to treat your room, or if your room is good you may want to compress the part a little more.

If it's too loud only in specific parts of the song use automation.

It almost sounds like your overdoing your fader adjustments. try lowing the bass only half of what you think is required.
It certainly could be bad monitoring or room.
I can't really remember back that far, but I think I may have had minor issues with mixdowns not being perfectly balanced.
But I did a lot of reading before I even purchased my first 4 track deck. I had a good idea how to start from educating myself about engineering. This is where we all start. Buy learning the craft,  and expecting it to work without understanding why is asking a lot. 
Having Monitors you've learned to trust is huge in having successful mixes every time.
 
 
 
Once you trust your monitors, mixing is a pretty simple process.
You sit and listen and adjust while keeping an eye on your master level.
2 tracks or 50 it's all the same process. 50 just takes longer.