What do you mean by, "I go usually on adapter and set charging max to 60% to protect my battery" ?
If by that you mean, you usually only charge your battery to 60%, then you are not doing your battery any favors. Li-Ion batteries work best and last longest when kept topped up to at least 90%, and are usually permanently damaged when drained too far. If you want your battery in your laptop to last as long as possible, keep it near fully charged as much of the time as you can. If you have no reason to run the laptop without the adapter, do not do so.
Also, laptop batteries are supposed to have an internal "gas gauge" like feature, which reports the status of the battery to the computer. Over time, this gauge actually loses accuracy. Some laptops such as Dell have the ability to periodically recalibrate the meter, and it's recommended to do so about once a month, by completely draining the battery then fully charging it again, while the status of the battery is being viewed by Dell's calibrating utility. (I believe it was in the BIOS last I saw it)
What it sounds like is, your battery is out of calibration and is reporting the wrong charge status to the computer. When the voltage starts to drop on the battery, it's likely your laptop is picking up on this and triggering the low battery status. Whether this behavior is because your battery is defective, out of calibration, or just worn out, I can't say, but it sounds like it's time for a new battery and better charging habits.