How do you know when to replace a tube?

I disagree with tube replacement. As said by Philjolet old tubes will get "boring", not bright. New tubes may actually make your system sound even worse, depending on what you buy.

2 things I can think of:
First-Klipsch can be fatiguing after a while. They may sound great at first but after 15-20 minutes your ears grow tired. These are really accurate and sometimes overly-revealing speakers.
Secondly-It could be your cartridge alignment. If the first half of every album sounds great but once the need approaches the halfway point or so on an album it may be tracking funny. THIS IS MY GUESS. Make sure your cartridge is properly set up by a pro.

Elevick makes a fair comment. I agree with the adage "if it ain't broke, don't fix it." Sure, check the cartridge alignment.

However, I do caution that if the power tubes are old, they are susceptible to failure, which in some cases could take out bias resisters. I would still ask the prior owner the age of the tubes. If the hours exceed factory recommendations, I suggest replacement.

BTW, is the amp old?? There's a couple of threads running about cap failure, particularly electrolytics. Just a thought.

FWIW

See if you get the same results with a different source like a CD player. If the same thing happens with CD's then it may be tubes. Tubes can change with temperature and not always for the better. However, when you own tube equipment it is always a good idea to have spare tubes on hand.
The other thing that comes to mind is your AC power. If everything else checks out ok you may want to try a power conditioner.

Change in sound between parts of a record side have nothing to do with the tubes--that is either something in the recording itself or a problem with cartridge alignment.

Unless you have access to a really good tube tester, the best way to determine when any tube needs replacement is to get a complete set of new replacement tubes as back up. Once in a while, replace the tubes with the new set to see if the sound has changed signficantly. Don't do all the tubes at the same time because that won't tell you which are beginning to go bad. I would start with the power output tubes first (they tend to have the shortest life), then try the small signal tubes. If the sound comes to life with a replacement, you know that the replaced tube(s) have started to go weak. Sometimes, older, weaker tubes also start to become noisy; if a good cleaning of the tube pins does not cure noise, it is probably time to replace the tube.

This is a bit off-topic, but not by much. I have a Sophia Baby that I have upgraded all the capacitors on (I just bought the ones Richard at Sophia recommended). I also bought a pair of Western Electric 396a output tubes. With these few upgrades, your Baby will sound much, much, better, you will be very glad you did them. You can do this yourself, as I did, or send it to Sophia, and they will do it for you. The WE tubes, NOS, are very expensive, so I found a good used pair for much less money. I have been using this amp for about a year and a half, with no problems.

This may or not be of interest to you, but it's something to think about, if you are going to re-tube.

Best of luck to you,
Dan