If someone is interested, there is my own solution with autocommands:
function! ReportFileSaveTime()
" Saves current time and file to a certain file
call system('echo `date +"%Y-%m-%d %H:%M:%S"` ' . @% . ' >> ' . g:fileSaveLog)
endfunction
au! BufWritePost * call ReportFileSaveTime()
let fileSaveLog='~/.vim/filesave'
Then you can, for example, $ tail -n 30 ~/.vim/filesave
to see 30 last file save time marks.