But anyhow, I already tried hardwiring the varaiable ala.

if (Read_Request_Time.at(i).size() > 0)
out << "Read_Request" << "\t" << "123,456,789" << "\n";
And it crashed or not ?

I really want to help, but its difficult to do so as I only see code snippets out of context, which should be ok under some default assumptions ( like: i is local variable in some kind of loop, that cannot be modified elsewhere ( same for Read_Request_Time list ), i is in valid range, only one thread is accessing them at a time ect... ).
Do you use threads in you code ?
By looking just at those snippets it's difficult to tell whats wrong, because they look ok.