Bottom line, there is no law that says an employer has to reimburse you, unless that reimbursement is covered in your employment contract.
Most employers will take a flexible approach unless they are in a cost-cutting phase (even then, if you can show that your training course will allow you to do both your job and that of the smelly antisocial guy next to you that the manager hates, the manager will probably swing to the cost of the certification materials, on-the-job training time and exam, with a contract caveat that you will be liable for those costs if you voluntarily leave the company within 2-3 years), but it is a relatively simple balancing act:
What added value will this certification provide to the company vs. what is the cost of the certification process in materials, lost work hours and financial expenditure.
Also, how easy is it to replace you with a lower/same paid person if you decide to leave should the training request be turned down; or will this training course make you more likely to stay with the employer/more likely to leave or be head-hunted.
Working as a consultant, certification in relevant and recognized skill areas helps my company open opportunities with other clients, or new areas within the same client. However, if the company does not get any more per-head revenue for those areas then I am not going to see any direct financial benefit (maybe something unofficial, that the company can write off against tax, but that is about it).
Fundamentally, the company has to earn enough from my contract to pay me and make my mandatory benefits contributions. If the contract mandates 40 man-hours per week for X, then that sets a ceiling for my remuneration. If my certification does not enable the company to renegotiate the cost of the contract, then my employer has to reduce their share of the pie (make less profit) in order to reward me. However, if that certification makes me more attractive to another potential client who is willing to cover my contract at 40 hours per week for 1.5*X, then the employer can move me to the new client, give me a pay rise, and bring in a new body to replace me. The old client may not be too happy to lose me, but the contract is not for MY services at 40 hours per week, it is for 40 man-hours.