Well, the reason for needing a new flu vaccine every year is because of the existence of multiple strains. You don't know which strains are going to hit this year. Based on data on ongoing infections a flu shot for each year is designed. And it's not just the existence of multiple strains, all these strains are also pretty dynamic. They keep mutating and undergo antigenic shift (a mutation that won't allows antibody that recognises previous strain to bind to a new one). So a vaccine that worked last year for a particular strain may turn obsolete if that strain has undergone an antigenic shift.
The idea to avoid or at least minimize such drug resistance or antigenic shift is to design drugs or vaccines against highly conserved viral parts. These are parts that need to interact with host proteins for example. Hence, any changes in the structure via mutation in viral genome will severely distort the functioning of virus itself. At least that is what the aim usually is when picking a drug target or a subunit for vaccine. It's challenging but a sensible approach.
Finally, I am not aware of data on increase in flu deaths correlated to flu shots. Sounds doubtful. Do share a link for that data, I can have a look into it.
Also, thanks for reading my post and asking such interesting questions. Do leave them here if you have more.