It makes perfect sense to me. The battery saver app probably turns the radio gain down which will conserve a lot of power. I don't use any battery saver app.
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Its must be a Fine Line with the Radio Signals gearing Down to Conserve Battery Life...Connections with Radio Frequency for Internet connection is definitely impacted by it...
The only Batter Saver I am using is Juice Defender Ultimate...I'll pick up as much as 2 hours on Aggressive Settings...Extreme to conserve more Live...It Buries the Bone to deep for Good Connections and Interrupted with drop connections...
IMO my friend...