Mac book Pro Does not Switch On and Show Charging. Charger keeps Blinking Orange and Green

I have an issue with my Mac book Pro 13" . When the mac is on work fine and show charging. But sometimes when I shut down mac, Next time it neither switch nor show charging on and charger keeps on blinking green and orange. But at a sudden after some days when plug charger it start showing charging and switch on normally and start working fine but again after some time or days same problem occur. This does not happen every days but after some days like 20-30 days approximately. Regarding this I have done every possible things like SMC reset, Charging with different adapter etc but all could not resolve the issue.

I observed that when I shut down mac with less charging left it switch on in less days with compare to more charging left, like if I left 5% charge then it will switch on and start charging withing 6 to 7 days but if i left more charge then it will take more time like 20% then it will take approx 15 to 20 days. so for using mac next time I had to wait for many days depending on charging left during shut down which hamper my work. If I use mac then shut down with very low charging left like 1% or 2%, it switch next time after connecting charger in very less time like 7-10 hours and work normally so if i need use mac either I do not switch off it or I have to switch off it with very low charging left like 1%.

I found somewhere on internet or youtube same problems with many cases, what they suggest to resolve this issue is that to unplug the battery connector which is inside the case and also showed in video with an example which resolved theirs issue.As my mac is covered under warranty so i decided not to do such things.

So I want to know what is this issue, is due to adapter or battery. as my Battery has depleted and completed more than 1200 cycles.

As my mac is under warranty, I left it at apple service center , but they are saying that this is Battery issue and telling to replace it but my battery is charging and working fine when mac is switched on. This problem only occur after shut down and after complete discharging it again start charging, switch on and working fine.

So please suggest me, what to do to resolve this issue and sorry for long question.

Thank you in advance.