I probably would not have received those days off.
I may not have received those days off.
I wish I went to Okinawa in Spring because it was raining when I went. I did not request days off in Spring, however, because I just started working with my company around that time.
ご質問の文章を全て訳すと、このような感じになります。英語圏の会社ですと、休暇が”取れない”ということはなく休暇は”申請する”か”申請しない”かで決まりますので、上記の例文ではrequest days offを使っています。