Don't do it in real time. Don't use tail -f which seems to me the problem.

Once an hour, or whatever, use tail to save the end part of the log file that has not been examined before. Save the end part to "tail.txt" for example. Use grep -C on tail.txt to get the context for each error line detected. Record total number of lines in the log file. Suppose there are 1000. Next time (in an hour), tail starts with line 1001 (or maybe 991 to make sure you have context).