假设条件：

• 如果我们创建一个新文件（restart.log）就可以了，否则我们可以在$LOG后面追加一个新行
• 我们将每10分钟（即600秒）仅执行一次restart尝试
• OP希望追加到当前$LOG（每次脚本运行时，当前代码覆盖/替换整个文件）

拟定方法：

• 使用新文件存储尝试最后一个restart的历元时间
• 在尝试restart之前，我们将当前历元与保存的历元进行比较，并且仅在历元的差异大于600秒时才继续（使用restart）

修改OP的当前脚本：

#!/bin/bash                                        # add "/" at start of shebang path

URL='http://some-url-here/'
LOG='/var/log/nginx/health.log'

RLOG='/var/log/nginx/restart.log'
touch "$RLOG"

wget -q $URL

if [ $? = 5 ] ; then
    echo "$(date). SSL Error." >> "$LOG"           # replace ">" with ">>" so that we append to $LOG

    read -r prev_epoch < <(tail -1 "$RLOG")        # retrieve epoch of last restart attempt
    prev_epoch="${prev_epoch:-0}"                  # default to 0 if there is nothing in the file

    printf -v curr_epoch '%(%s)T'                  # use printf builtin to grab current epoch and save in variable 'curr_epoch'
    # curr_epoch=$((date '+%s'))                   # uncomment if 'printf -v' is not available in your system

    delta=$((curr_epoch - prev_epoch))

    if [[ "${delta}" -gt 600 ]] ; then
        sudo service nginx restart
        echo "${curr_epoch}" > "$RLOG"             # replace ">" with ">>" if you want to maintain a history of restart epochs; the "tail -1" should insure we only grab the 'last' entry
        exit
    else
        echo "it has only been ${delta} seconds since last restart attempt; skipping restart" >> "$LOG"
    fi
fi