I was, according to the National Labor Relations Board (NLRB) Administrative Law Judge that heard my case, illegally terminated from my job of 28 years.

I was fired approximately 1.5 years ago and my case is currently being appealed by the employer to the full NLRB in Washington, D.C.

I am wondering if there is any statute of limitations regarding bringing a separate civil lawsuit and whether or not a pending action affects the running of the statute?

I understand that they, pending their loss of this appeal, have two more appeals possible (Federal Court and then Supreme Court) and that the process could drag on for several more years.

Any information will be greatly appreciated.

Whether you even have grounds for a civil suit and if so, whether you are within the statute of limitations to file on those grounds is something you should be addressing with your attorney.

Wouldn’t worry about that. In general Board cases in unfair labor practice proceedings have been upheld in whole or part by court of appeals 80% of the time. An employer who fails to comply with a court of appeals enforcement order risks a contempt citation.
A Final review possibility is a writ of certiorari from the U.S Supreme Court.
A board order is not self-enforcing: that is the Board has no coercive power to compel adherence to its order. Section 10(e) of the NRLA gives it the authority to petition Court of appeals for enforcement of it’s order . Under Universal Camera v NLRB (U.S 1951) the Supreme came up with this review standard:
2. In amending 10 (e) of the National Labor Relations Act so as to require that, on judicial review, the Board's findings of fact must be supported by substantial evidence "on the record considered as a whole," Congress made it clear that a reviewing court is not barred from setting aside a Board decision when it cannot conscientiously find that the evidence supporting that decision is substantial, when viewed in the light that the record in its entirety furnishes, including the body of evidence opposed to the Board's view. Pp. 487-488. (Cut Paste Courtesy West Group)
This basically means that the court of appeals can assess not only the facts supporting the board decision, but any pointing to an opposite conclusion as well.
Since 10(f) of the NRLA provides either party may petion the Court of appeals for a review of the order.
This is what has happened in your case the employer wants the Appeals Court to review the Boards findings. They hope that the court will find in their favor.
Now as far as a supreme court challenge “and this is where it gets good” under Universal Camera v NLRB (U.S 1951):
4. Whether on the record as a whole there is substantial evidence to support agency findings is a question which Congress has placed in the keeping of the courts of appeals. This Court will intervene only in what ought to be the rate instance when the standard appears to have been misapprehended or grossly misapplied. P. 491. (Cut Paste Courtesy West Group)

Here the Supreme Court is addressing itself in the underlined this is good for both parties but the Supreme Court will only hear the case under narrow circumstances.
Your case the Board has found in your favor that is good. Now for the part about filing suit on your own. Why? It does not make sense. Why would you pay for a lawyer when the board has found in your favor. Therefore the appeals attorney will be paid by the NLRB.If for the remote possibility; the employer makes a Supreme Court challenge. Do you know how much money it would cost? Now who has more money you or the U.S government?
My advice in this case is you have an attorney already be patient, even if it does take time.
JoeC