A trustee has a legal obligation to carry out the terms of a trust. That being said, Where, as here, it appears that the Trustee has discretion to distribute principal as he, she or it deems necessary (i.e., for "to maintain the beneficiary [in a manner (text added)] in which she is accustomed..,) rather than according to an ascertainable standard, a beneficiary might be able to convince the Trustee to exercise that discretion. However, success is not guaranteed.
Thank you for your question. The language you quoted appears to give the trustee considerable discretion when, and to what extent, he/she should use principal as a means of supporting the beneficiary. If it is obvious that dipping into principal is necessary and that anyone serving as trustee would realize that, you have one of two options: (a) try to persuade/negotiate with the trustee; or (b) bring a petition in the probate court to have the trustee removed. The latter is a course of action I would recommend only after the former is exhausted, as such proceedings can be time-consuming, slow and costly. However, courts have removed trustees where they acted in deliberate disregard of the beneficiary's interests and needs.
A discretionary trust leaves the beneficiary with little out-of-court recourse if your trustee is not willing to make any distributions. If you have reasons for the requested distribution which fall within the limitations you have disclosed and the Trustee ignores your requests; you may cause to go to court and ask a judge to require the trustee to make the distributions you request, or in the alternative replace the trustee. A flat out denial of your requests may become a breach of the trustee's fiduciary duty owed to you under the terms of the trust.
However, if you may unreasonable requests the trustee may be within his or her right to deny your request.
In order to avoid this type of problem I recommend the use of a trust protector or distribution trustee. Based on what you have told me, it is probably to late to have that type of arrangement put into effect. However, if you can determine why the trustee is not making requested distributions you may be able to reach an out of court accord that will get you what you need. I believe that without experienced counsel you will not get the result you desire and you really should visit experienced trust counsel for the best results.