Can a non-compete agreement be enforced if your employer stops providing benefits as outlined in your offer letter?

1) The non-compete most likely can still be enforced against you. Even if you are no longer receiving all the compensation or benefits you had been, you are still employed; that continuing employment would most likely still be enough to make the agreement enforceable. (Employers may change compensation, including reducing pay, afte all.)

However, as noted, it is only "most likely" that the agreement is still  enforceable--if the offer letter to which you refer was sufficiently strong and detailed as to constitute an employment contract requiring you to receive certain compensation or benefits, then in that case, the employer's breach of its obligations would likely free you from your reciprocal obligations. Most offer letters do not, in fact, form enforceable contracts--however, it is possible that yours might. Therefore, you should bring the offer letter and the non-competition agreement to an employment law attorney, who can review them and the circumstances of your employment (including the circumstances under which you took the job) to see what your recourse is.

2) Also note that if the offer letter forms an enforceable contract, or if you relied on the employer's promises about a per diem, travel time, etc. in taking the job, and in so doing did something significant to your detriment (e.g. left a different job; relocated), then you may be able  to require your employer to continue honoring its promises. (Note--the legal theory for holding someone accountable to promises which you relied on to your detriment is call "promissory estoppel"; there are a number of different circumstances or criteria which must be fulfilled for promissory estoppel to apply, but your lawyer can review your situation against them.)

3) While non-competition agreements are enforceable, if they are too long or too broad in scope, courts may reduce them to a more reasonable level (called "blue penciling" them). For most non-senior-management employees, a year is usually about the limit for a non-compete, so the non-competition agreement you describe may be too long; it therefore may be subject to being judicially reduced if necessary. Your attorney can discuss this with you, too.