Some things I noticed were wrong with your plugin.
1. Line 77: if (args < 1)
should be if (args > 0)
If there is only one arg, you can use GetCmdArgString();
Nevermind, you want the first arg, and only the first arg in this case.
3. Line 87: if (StringToIntEx(arg1, amount) < 0)
look at the return for StringToIntEx(); -- it's not what you want right here.
Try the following code instead:
new amount = StringToInt(arg1);
if (amount < 0)
4. You have the check on Line 87 for if the amount is < 0 and it returns Plugin_Handled in that section. That means the check on lines 93-96 are useless. There will never be a positive answer to that if statement.
5. Line 105: ServerCommand("%s", arg1);
should be ServerCommand("addtime %i", amount);
6. You should probably use LogMessage(); instead of LogAction(); in the two cases you use it.