I have found that what kernel resource ran out on the client mail server was the number of open files.  I’ve bumped that up by 5x, hopefully that will be sufficient.

Dec 3 08:57:22 mail kernel: [371342.776244] VFS: file-max limit 194527 reached
Dec 3 09:43:33 mail kernel: [374113.872327] VFS: file-max limit 194527 reached
Dec 3 09:43:33 mail kernel: [374113.905264] VFS: file-max limit 194527 reached
Dec 3 09:45:17 mail kernel: [374217.999876] VFS: file-max limit 194527 reached
Dec 3 09:45:23 mail kernel: [374223.425007] VFS: file-max limit 194527 reached
Dec 3 09:45:24 mail kernel: [374224.590837] VFS: file-max limit 194527 reached
Dec 3 10:21:11 mail kernel: [376372.038404] VFS: file-max limit 194527 reached
Dec 3 10:21:24 mail kernel: [376385.096118] VFS: file-max limit 194527 reached