Ted
I’ll pass along what I have found/learned on RV batteries and leaving the TT plugged in all the time. Leaving the actual power converter plugged in I have not found any issues, however leaving the battery disconnect on, that I have.
The 12 volt converter most coaches have, unless you upgraded or ordered it special, work well at creating a good supply of 12 volt power to run the camper when plugged into shore power. They do offer battery charging as part of this. However they are not great long term for your battery if left connected regularly. Basically they are not great battery chargers.
Your 2004 camper may have a CS6000XL or the older Centurion CS6000. See here floor there web link.
http://americandirect.ibuilder.com/a...ns&NID=1466143
Right around that 2003/2004 time frame some Sunlines had the older CS6000 or the newer CS6000XL. Since I upgraded my TT this year with another 2004 model, well I just happen to have one of both…..

The newer to me camper has the older model, and it has a bad set of fans in it that sound like a mack truck grinding away. errr.

So I have a fix it project to do.
The newer CS6000XL has some more features, however it does not have a float feature that I can find. The float feature keeps a constant voltage on the battery so it will not discharge away when not in use. There is not much current with this float type charger once it reaches full charge and as such it does not boil out the battery if left on full time.
The standard converter can cook out your battery if left connected on shore power for long periods of time. What is a long period? Pending on your battery health, it can be days or weeks. I actually turn the battery disconnect off at the campsite if I’m staying many days. I leave it on long enough to get it fully charged off the TT charger then turn off the disconnect. As these American Centurions models we have will not shut off completely.
Ideally for winter storage, take the battery out, bring it into a warmer then outside place and put a float charger or better a battery minder on it. Before putting the float charger on, charge the battery all the way up with a normal charger then put the float charger on. The newer battery minder Plus systems also has a desulphation feature on it. This feature boosts the voltage up to 14 volts to burn off sulfate that builds up on the plates. This desulfation process helps extend the life of your battery.
You may also hear about a trickle charger. The float charger is still different then the trickle charger. It is better then the normal charger or converter battery charger but it still does not shut off and if left on long enough it too can cook the battery. It just takes longer then the converter to do damage.
If you do not have the Battery Minder or float charger, then actually just charging it fully up, take the charger off and come back and do it again in a month is the about the next best thing, again storing somewhere warmer then outside.
Here is a pretty good web site written in easy to understand terms. It is called the 12 volt side of life.
http://www.ccis.com/home/mnemeth/12volt/12volt.htm
Most campers do not think about the converters and battery charging as the dealers never spend a lot of time on it and the standard converter does work, just it does not do your battery true justice and slowly over time does it in.
I’m not a battery expert by any means, but I have bumped into this a while ago and found there is a lot I never knew and I’m still coming up the education curve. However with everything I have researched, leaving the battery connected to a standard type TT converter for long periods of time is not a good thing.
See this one brand of higher end power converters for wet cell batteries. This Progressive Dynamics Inteli Power PD9260C unit has the high end charger plus the converter. It has 3 stage charging, has the desulfation and float mode system all built into it. This type you can leave powered on all the time. Folks who boondock a lot use these as they drain their battery down more then most who use shore power most of the time and a better charger is easier justified.
http://www.progressivedyn.com/power_...ters_9200.html
However it costs about $200 just for the converter/charger which is what our entire $197 CS6000XL converter, DC fuse strip and 120 volt breaker system costs. In this case you get what you paid for.
Hope this helps
John