While there are still placements to apply for, never give up. You've come this far and it would be a shame for all those painstaking hours making applications and preparing for interviews to go to waste. I'm working with many students like you right now and their shared attribute is resilience; the will to succeed and achieve their goal. Between now and September many of them will get the placement offers their dedication deserves.
It doesn't matter when you secure your placement, it is seeing through the task and getting to the finish line line which is most important. It takes guts and determination to keep going when others have already finished The Great Placement Race but keep going and your Placement Officers will be cheering you from the sidelines.