Mail and Gmail

The Mail on my mid-2011 iMac is having a problem with Gmail. This is a very recent problem My OS is the High Sierra Ver 10.13.6. Mail does not allow my three Gmail accounts to go online unless I re-enter the passwords each day. This started happening 6 days ago. My Gmail opens up fine on my Mac Air and my 2019 iMac. I find this a bit confusing. There is nothing wrong with my older iMac as far as operations go for my basic needs. I see no reason to bench the unit just because of this Mail/Gmail issue. Any suggestions for a solution would be appreciated.