I was asking the question in general terms, but I will answer your questions about my specific situation.
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First, we need to define "constant." If you are not doing the exact same TSS-point workouts every day, your CTL will vary. Do you mean the same every day? Or within a certain margin every week? Or within a certain margin every month? The same exact CTL every day is almost impossible in reality
From March to June my CTL rose from 40ish to 100ish. I call that a period of increasing CTL. From June to September my CTL ungulated between 90 and 110. I'm calling that a period of "constant" CTL. No it's not really constant, but it's average value over several months is near constant.
How often are you increasing your training zones? Every day? Every two weeks? Every six months?
I did fitness tests in March, May, June, July, and October. I adjusted my FTP after the May and June tests. The July and October tests showed no improvements, so I did not adjust my FTP.
Next, where are your TSS points coming from? Are you just doing long steady endurance rides? 2x20s? VO2 intervals? Intense group rides? Are you doing recovery rides with 5-second max sprints to try to trick the TSS point system? What makes you think that any level of CTL will have a direct effect on your FTP?
In March I started with L2 stuff. In April I switched to a plan modeled after the 1st case study in Training and Racing with a Power Meter. This consisted of a mixture of intensities and volumes. For example, a week might go like this: M rest T 6x2(3) W 2x15(10) Th L3 + NP bursts F rest Sa Race Su 3 hours L2. However, all of my weekdays were split into 2 workouts, so if a day called for 6x2(3) I did 3x2(3) in the morning and 3x2(3) in the evening. I also did a 1 hour gym workout once a week, but it was not focused on helping my cycling. I worked for 3 weeks and then rested for 1 week. The testing was done at the end of rest weeks. My ATL and TSB had a very regular 3 weeks up 1 week down pattern.
In July, August, and September, I participated in many events/races, did a couple multi-day bike tours, had some multi-day recoveries, and my training became less routine. My ATL and TSB had a fairly random pattern. CTL in September gradually declined to 80ish. September is a busy month in Minnesota. Everyone rushes to party outside before winter hits.
In October I switched to 6 1x20 at 90% FTP workouts during the work week, a 3-5 hour group ride or solo L3 ride on Sat and a 2-5 hour L2 ride on Sun. Monday is gym day and Friday is rest day. My CTL is currently 80ish and rising.
In order to keep your CTL constant, that means your ATL and TSB would have be constant as well. At that point, why would your FTP be increasing at all? You are not imposing any new demands on it. With a "constant" CTL over a longer period, say 8 to 12 months, it's more likely that your FTP would be decreasing not increasing,
You have more or less answered my first question. What about my second question? What does one do if raising CTL higher is not an option?
If it is true that fitness only increases when CTL is increased, then it should be possible for a sedentary person to reach their genetic potential in 3-6 months, because CTL can easily be increased from 0 to 150ish in that time period, no? However, I've never heard anyone claim that to be true. How do I reconcile this apparent paradox?