Because my phone had been running out of batteries for a while, so I thought it would be better to save your number on another phone, this way I could reach you.

This sentence was used to describe an event that happened two days ago.
Hi,

Because my phone had been running out of batteries for a while, so I thought it would be better to save your number on another phone, this way I could reach you.

This sentence was used to describe an event that happened two days ago.

Because my phone had been running out of batteries for a while, I thought it would be better to save your number on another phone. This way I can reach you.

Clive
PreciousJones......my phone had been running out of batteries for a while....,
This doesn't sound syntactically logical to me.

My cell phone ran out of bettery, so I couldn't call you back - Battery depleted, not operable. Ok

My cell phone was running low on bettery so I had to call you back on a land line - Ok

My call phone has/ had been running out of bettery....- Not good! If the battery was in fact out, using "perfect progressive tense", past or present, makes little sense to me.