I've had similar slow growth of the baby when brewing in an area that
was too cold for them, even having one batch which formed a mold at
the top which I threw out (not worth the risk).
The SCOBY thrives in a warm, dark environment. The best place I've
found is the bottom cabinet of a china hutch, which my wife kicked me
out of because the Kombucha smell started to permeate the hutch after
a few generations.
I have used just the starter cup from the previous tea batch for the
new batch. This method does take longer to form the SCOBY and the
resulting tea is not very potent, but it will get you by for future
generations.