If you do it via Bitcoin Core, it should show the error code and description for why your transaction was rejected.
Common causes are things like min-relay-fee not met, or dust outputs, or possibly it is just using a UTXO that is unconfirmed and at the end of a long chain on unconfirmed transactions etc.
Next time, try using the debug console (Help -> Debug window -> console) and "sendrawtransaction" within Bitcoin Core to see the reason your transaction is being refused.