Slow clock in Windows, causing problems with Outlook 2010 reminders

My work laptop is a Dell Latitude E5550, running Win7 Enterprise SP1, with
all the latest Windows updates. FWIW, this has an Intel i5-5300U CPU and
8GB of RAM. It is docked all day long and the Processor Power Management
"plugged in" settings in Power Options are a) Maximum Processor State =
100%, b) Minimum Processor State = 100%, and c) System Cooling Policy =
Active. This was a brand-spanking new laptop as of 4 months ago. From
day 1, I've had problems with getting Outlook reminders in a timely
fashion, sometimes even after the meeting has started. If I set the
reminder one hour ahead, it will usually show up 45 to 55 minutes before
the meeting, so I set all of my reminders at least one hour before the
meeting.

Eventually, I noticed that Windows' clock was losing time over the course
of the day. So, while the time might be correct at 8am when I power up, by
10am (actual time), the Windows clock will read 9:55am. I suspect that
this is wreaking havoc on Outlook's ability to issue reminders in a timely
fashion. Note that, even though I'm losing only a few minutes every hour,
I'm still getting reminders 10 to 40 minutes late. I found a few "repair"
options for Outlook, but these did not resolve the issue. I am told that
all of our PCs ping the network time server every four hours. So, I set up
a task in Windows Scheduler to ping the time server every 5 minutes. While
this helps keep the Windows clock within 40 seconds in any given 5 minute
interval, I'm still having problems with reminders showing up on time.

I'm of the (internet-educated) opinion that the battery on the laptop's
motherboard is bad. I asked IT support if they could give me a new unit
and swap in my hard drive to see if that resolves the issue. But they want
to delete my Windows profile then recreate it, which means that I'll have
to set everything back to the way it was. I am trying to avoid this. The
unit is still under warranty, so I'm not sure why they don't just get Dell
to replace it. I even offered to replace the battery myself, but was
warned that "we rarely take apart our laptops".

Any ideas I haven't already considered?

- Dan