I'll give you a very, very, very weak maybe.
IRS regulations very strictly regulate when an employee can switch from one plan to another. It can be done when one spouse first becomes eligible for benefits and during the annual open enrollment. Other than that, there has to be what is called a qualifying event (also known as a life event). Normally the fact that claims are being denied is NOT a qualifying event and thus you would not be able to make a change until the next open enrollment.
A great deal is going to depend on why your employer has stopped paying. If it's simply because it's a limited benefit and you've used it up, then no, you cannot change at this time. If, however, your employer has changed the plan design and a benefit which formerly was covered is no longer covered for anyone (not just you), then MAYBE it might qualify as a "significant change in coverage" and MIGHT be a valid QE. Your wife's employer will be the ones to make the call. There is no bright line for what constitutes a "significant change in coverage" event and you will have to provide written evidence of the change, including copies of both the old plan and the new. Even then, it is very, very, very much a long shot.
Do not waste time because even in the unlikely event that this qualifies as a "significant change in coverage", you only have 30 days from the date that coverage changed to complete ALL the requirements for enrollment. (Actually, it might possibly be one of the rare situations where it's 60 days - I'll have to check with our compliance officer tomorrow - but 30 days is all you can count on under the law.)
Finally, please keep in mind that this is Federal law and the employer will be the one to face fines and penalties if they allow the change in error. There's not much of a chance that this will qualify and they have very little discretion in the matter. It will not be a matter of the employer being obstructionist if they refuse - it will be a matter of the employer following the law. This is going to be a catching flies with honey situation - they have little incentive to allow the change, significant penalties if they allow it in error, so you want to encourage them to use what very little discretion they have.
For the record, this is precisely what I do for a living.
Good luck.