is lack of representation by an attorney, meaning he did not competently do his hob, a basis for appeal on a decision made at a hearing without oral argument?
The short answer is probably not. The long answer is appeals are based on issues of law only, not issues of fact. Criminal cases may be appealed on the basis of incompetent representation of counsel but this is not available in a civil case. You may be able to appeal on another basis and only a qualified attorney can review your case and figure this out. This is a complicated area of law and will be expensive for a couple of reasons. The attorney must first order the complete trial transcript and review that for "legal errors". The transcript is expensive. Legal errors are errors committed by the court, NOT BY your lawyer. For example if the opposing side brought in some evidence which should have been excluded, and your attorney made a proper objection, and then made what's called an offer of proof (Demonstrating to the court, often without the jury) what the evidence would show AND that evidence is likely what made the difference in the decision, THEN you have an appealable issue. If your attorney just didn't win, or didn't do exactly the job you were expecting that is not going to make an appealable issue.
Also, you didn't mention what area this case was in so that makes a difference as well. You need to have both a good case and a fair amount of money to appeal a case past the trial court level.
This is meant as general advice only and does not create an attorney/client relationship.
I read this a little too fast. Since this was done without oral argument there is NO trial transcript. This is almost impossible to appeal unless there is no case law that supports the Judge's opinion. I'm sorry but this is one where you will probably lose.
The answer will turn in large part on whether this is a civil matter or a criminal matter. If it is a civil matter, then it is extremely unlikely that you will win on appeal. The better option would have been to have retained new counsel and moved for reconsideration within the applicable time period. If it is a criminal matter, then you may seek a writ of habeas corpus, which permits the investigation into matters outside the record as a grounds for the appeal.