Am I being unreasonable

Hope I’ve posted this in correct place.
Feeling really low at the moment.
Here goes... my youngest DD and family live in Australia and I booked a ticket to go and spend Christmas with them leaving 22nd December back on 19th January. However my employers are not authorising my time off due to me working in retail and it being our busiest time. Our contract says we are only allowed to have extended leave once in 5 years and I’ve already used this up when I visited them in 2015. I work 10 hours a week for a large greeting card company who franchises in a well known supermarket. I have arranged cover whilst away with a buddy and non of my work colleagues have any issues with me taking this time off. I’ve been with the company 12 years and rarely had time off and I’ve got 5 weeks holiday free to use.Ive been informed by my manager that I will have to leave the company and she is going to advertise my job.Im 61 and single and don’t feel I’m asking got to much maybe I’m asking them to be more understanding but this has taken the edge of the excitement of going to visit them. My DD and I have spoke and she is concerned about me loosing my job and we both ended up in tears. Should I just think sod it im not getting any younger and one day may not be fit enough to make a 23 hour flight alone or am I being unreasonable.