In English we far prefer to negate the main verb in the matrix clause in sentences like this. Negating the infinitive is generally awkward unless extreme technical specificity is what is required. Compare:
- I want to not go.
- I want not to go.
The original is better because it negates the main verb and not the infinitive. It is easier to process.
The original Poster is using the phrase no longer to negate the sentence. They would be far better off with:
- This no longer appears to work in any web browser.
Here the negation is applied to the clause headed by the verb appears, not to the infinitival clause.
For the record, as it will no doubt be a matter of some debate here, there is no reason not to split an infinitive if it sounds right to you.