This happened to me some years ago and I'm still not sure what the proper course of actions should have been.
Just to give you the context, I used to work in a medium-sized company with a small software division. This was in a small town in Spain, with very little opportunities and basically no inflation.
After 2 years working as a developer without a raise I had a discussion with the head of the software division (my manager's manager) about my future growth in the company and I was basically told that the following year I was to receive a raise and more responsibilities. I explained that I was especially interested in QA (where I already had some experience), since our software had a terrible rate of bugs and nobody seemed to knew how to fix that and the reaction was quite positive.
Flash-forward one year and I had a meeting with this manager were I was given a raise (3%, I was expecting 10% to 15%) and the unofficial responsibility of QA. My first reaction was to instinctively object that the raise was much lower than what I expected and the manager just told me that I was never happy and called off the meeting.
The following day I wrote him an e-mail to thank him for the raise and the promotion and asking for another chance to discuss the raise and more importantly discuss the new responsibilities assigned to me with the new role. I was especially worried that since the company had no QA before, my role could have not received much attention and consideration. My e-mail received no answer.
After that it was barely announced to the rest of the team that I had this new qualification and I was not given any other direction (by my manager or manager's manager) about what was expected from me.
I spent the next few months trying to implement some new policies and procedures (tests, continuous integration, continuous deployment, usability tests, ...) but my direct manager was not really familiar with all this world and basically shut down most of my proposals as a bunch of time wasters. This was also done in front of other developers, by telling them to stop wasting time on tests and such.
After a few months I ended up leaving the company because of the lack of appreciation of what I was trying to do. When I resigned the managers's manager asked me the reason and when I tried to explain the reasons, the manager was surprised about it and told me that I should have communicated with him before what was going on. When I tried to remember him my e-mail after our first meeting his answer was that he was a busy man and so I should have sent more e-mails. I was basically told that it was my fault for not really pushing through with these new ideas.
Looking back at this situation I'm still not sure if I should have done more to improve the situation or if it was completely hopeless from the beginning. More in general I still wonder if, as I asked in the title, I should really think that sometimes managers are just too busy sometimes and sending multiple e-mails asking for the same thing is a reasonable strategy. What are your thoughts about this?
I'm adding to this question a detail that maybe is not clear. My guess was that the manager ignored my e-mail on purpose to avoid discussing the subject any further.