I would hope that you do not have Pop Peeper set to check mail every minute.
It is not recommended to be checking mail that frequently (if for no other reason than the Email Client would tend to look at this as suspicious activity).
If you haven't changed any settings then Pop Peeper wouldn't be checking mail every minute (my guess is that the default setting is either every 15 or 20 minutes).
Go to this setting in the Pop Peeper main menu: "Tools" > "Options" > Select the "Mail Check" tab and please post what the value is in "Minutes - Polling interval" (top left option in this window).
This value represents how often Pop Peeper is checking your mail.
Btw, how many email accounts do you have in Pop Peeper?
On a side note: If you're using IMAP and have "IDLE" enabled in your Pop Peeper email account(s) then for certain accounts (not all) that use the IDLE function this feature allows IMAP email users to immediately receive any mailbox changes without having to undertake any action which is irrespective of the "Polling interval" setting in Pop Peeper of course. But
this would not in any way increase your processor activity as you've described, so even if this were the case that you're email accounts are in fact using IMAP with "IDLE" enabled and "IDLE" is functional let me clear that this would
not in any way account for your high processor activity issue. I would think that your processor activity is due to something else other than Pop Peeper actually. Perhaps it is Windows Update if the processor activity fluctuates and at times reaches high levels more than usual. If you have not been processing Windows Updates so that the update list gets exceedingly long this can cause increasingly higher processor activity when Windows Update is running depending upon the computer. Another thing you might want to check on is the possibility of either Malware or a Virus of some kind that may be impacting your computer. Of course running a Virus/Malware scan on your computer will determine if this is an issue.