I object to praises that are too abundant and too often.
- Does the meaning of abundant fit here?
- Often is an adverb, so can it be used as a predicative which is
usually adjective or noun?
Abundant fits; it means present in great quantity; more than adequate; oversufficient.
Often does not fit; an independent adverb may not be the sole predicate of a clause. You could make the adverb modify an adjective (such as given) to get rid of the grammatical inconsistency:
I object to praise that is too abundant and too often given.
Or you could replace the adverb with an adjective:
I object to praise that is too abundant and too frequent.
However, all that said, there are many more words in the sentence than is necessary. For instance, abundant includes a good bit of frequent, so you could easily remove the last three or four words; also, [noun] that is too [adj] can often be simplified to over-[adj] [noun]. I object to sounds a little more judgmental than necessary: I would use I dislike. So the sentence now looks like this:
I dislike overabundant praise.
That sounds much better than the original.