In reply to Simos:
From personal experience I've found that training whilst not fully recovered has been ok for me. I've also found that shorter sessions more often are more beneficial. Stop climbing whilst you still feel strong. Climbing until you are feeling weak and easy moves feel desperate is likely to end in injury and recovery time will be too long.
I often climb on consecutive days even when my body doesn't feel fully recovered, however I vary what I am doing in my sessions. I usually follow a roughly structured training plan but sometimes its important to listen to your body and adjust accordingly. I may have planned to focus on finger strength but find my fingers are feeling a bit too tired or fragile, so I'll focus on power with larger holds or core strength and general body conditioning.
During times when I'm training hard and upping the number of sessions I do (sometimes 4-5 a week) my body definitely requires an adjustment period, I can't just jump straight into it, it needs to be gradual. After a bit of time I reach a point where I can train in the evening and feel mostly recovered by the next day. I am however a youthful student with little else to take my time from me (kids, job, etc...).
Earlier on in my climbing life I couldn't have imagined doing more than 2-3 sessions a week due to fatigue, but I realise now that my sessions were too long, unstructured and to be honest of little value. When I figured this out I saw big improvements, which quickly translated to improvements on rock too. During periods when I am training lots I will take rest periods every so often (up to a week long) in order to let my body recover fully.
To summarise:
Focus on short but more effective sessions, more often. Listen to your body. Vary what you focus on in your sessions. Stop strong. Take rest periods. Most importantly, if you are going to increase the volume of sessions do so gradually, let your body adjust.
Hope some of this is helpful to you
Post edited at 22:46