How do you implement a re-try-catch?

You need to enclose your try-catch inside a while loop like this: -

int count = 0;
int maxTries = 3;
while(true) {
    try {
        // Some Code
        // break out of loop, or return, on success
    } catch (SomeException e) {
        // handle exception
        if (++count == maxTries) throw e;
    }
}

I have taken count and maxTries to avoid running into an infinite loop, in case the exception keeps on occurring in your try block.

As usual, the best design depends on the particular circumstances. Usually though, I write something like:

for (int retries = 0;; retries++) {
    try {
        return doSomething();
    } catch (SomeException e) {
        if (retries < 6) {
            continue;
        } else {
            throw e;
        }
    }
}

Obligatory "enterprisy" solution:

public abstract class Operation {
    abstract public void doIt();
    public void handleException(Exception cause) {
        //default impl: do nothing, log the exception, etc.
    }
}

public class OperationHelper {
    public static void doWithRetry(int maxAttempts, Operation operation) {
        for (int count = 0; count < maxAttempts; count++) {
            try {
                operation.doIt();
                count = maxAttempts; //don't retry
            } catch (Exception e) {
                operation.handleException(e);
            }
        }
    }
}

And to call:

OperationHelper.doWithRetry(5, new Operation() {
    @Override public void doIt() {
        //do some stuff
    }
    @Override public void handleException(Exception cause) {
        //recover from the Exception
    }
});

Your exact scenario handled via Failsafe:

RetryPolicy retryPolicy = new RetryPolicy()
  .retryOn(NearlyUnexpectedException.class);

Failsafe.with(retryPolicy)
  .onRetry((r, f) -> fix_the_problem())
  .run(() -> some_instruction());

Pretty simple.