A few additions to enderland's great answer.
You cannot force your employer to grant you extended leave without any effect to your career with that company. Depending on how important the leave is to you, there are a bunch of strategies you can use to try to change their minds. At the end of the day, you will need to decide if it is worth losing your job over this, and choose wisely.
Check Your Contract
Read your contract to see what it says about leave.
- Is the employer allowed to dictate when you take leave?
- What happens to leave if it cannot be taken?
- What happens to leave on termination of employment?
If the employer is allowed to decide when you take leave, they have a contractual right to deny you taking leave at a certain time, which would mean they have the right not to allow you to take a long break.
At the same time, if your leave does not roll over to the next period, and/or you can never take the amount of leave dictated in your contract, then you have a slightly stronger case to argue (why give me X days if I can only use X - n days per year?).
In the worst case, if your contract is terminated, what rights do you have for remaining days (are they added to your leave period, are they paid out upon termination, are they lost, etc.)?
Before you figure out how to tackle the issue, be sure you know what your contract says your rights are. If you are within your rights to take an extended leave with notice to your employer and they are still denying it, you may have legal recourse (consult with a lawyer), but that will likely sour your relationship with the employer.
Ways to Convince Your Boss to Change His/Her Mind
If you aren't keen on taking legal action, and/or your contract doesn't allow it, you'll need to change your boss' mind. Here are a few ways you could try to do that.
Determine why your boss doesn't want to give you leave
Have an honest discussion with your boss about what the issues are with taking leave. Is it because things are particularly busy now? Is it because the department is understaffed? Is it because there is nobody equipped to handle your workload while you're gone?
Once you figure out why he doesn't want to provide it, you can work on solving those issues by waiting for a better time, training someone to take over while you're gone, or trying to figure out when the staff will fill out better.
The point is to determine what the reason is behind denying your request, and then doing your best to eliminate it. No guarantees that will get you the leave, but it is the obvious first step.
It may be the case that the company just likes to be stingy with leave, in which case you should skip the next suggestion. One way to find that out would be to see if anyone in the office has ever been granted an extended leave of the length you want to get. If so, it probably isn't against company policy.
Call Upon a Higher Power
If you still can't get permission because the problem can't be fixed (or the problem is that your boss just doesn't want to), you can try escalating it a rank. You can send an e-mail to your boss' boss, CC'ing your boss, explaining something like:
Hey boss' boss, I have a lot of leave saved up and would like to take an extended vacation. Unfortunately our team has a pretty significant workload and my manager can't spare losing me for several weeks. If any other team has some additional manpower, is there any chance we can make use of that to make sure the work gets done during my absence?
Be careful going over your boss' head, as it likely won't make him/her too happy. Be sure not to make your boss look bad, and imply that he is making this decision to look out for the company's interests though he really wants to grant your request.
If your company policy is to try to grant employee requests within reason, your boss will have a rough time explaining why you should be chained to your desk and not given leave, and will probably go the path of least resistance working with his/her boss to find a way to cover while you're gone.
If Push Comes to Shove...
As mentioned, your company may just be stingy at granting leave. If that is the case, you need to decide if you're willing to lose your job over this. If you are, then here are a couple suggestions. (If not, you need to accept that you cannot take a long leave, and take things from there).
Just take it
Send an e-mail to your manager informing him/her that you will be taking leave from date X to date Y (however many weeks you want within your contractually allowed leave), making sure that you are giving ample time for the company to prepare for that leave (don't say you will be leaving from 4 weeks tomorrow).
Hey boss, as you know I have 45 days of leave saved up. I will be taking vacation from July 1 to August 31 (40 working days). Over the next 6 weeks, I will be happy to get someone up to speed on my work so it goes smoothly while I'm gone.
In the worst case they will fire you and/or will not take you or your career path seriously after you come back. In the best case they will just let you take the leave because it is easier than finding someone to replace you (bearing in mind that butting heads with your manager probably isn't the best idea for career growth in any case).
Offer an ultimatum
If your boss refuses the above request or asks you to meet, you can raise the stakes a bit. You can tell them that you will take your leave or use your rights under your contract to have it paid out and give your notice on the spot.
Hey boss, I understand you don't want to give me the leave, but I really need to take it for personal reasons. If you aren't willing to grant it, I'll need to give my notice, and the company will have to pay out those days anyway.
This is not going to get you a recommendation letter, but it will put your boss in the rough spot of having to scramble to find a replacement for you, or of having to grant you the leave (at the minimum to give him more time to find a replacement).