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I'd consider running the thing down until it forces you to charge and repeating a few times to see if it resets the battery meter and lasts longer. Just to rule that out. If it's a replacement, or new, it's not unusual for a lithium battery to benefit from a few initial charge cycles by up to 30% or so in some cases.
An 11% drop for a sync is a lot, I think the most I've ever seen was around 4% on my Touch. Normally more like 2-3% on my Glo. OTOH, if the battery metering is off that would contribute somewhat.
Can't hurt to try.
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