Have you seen the description of the history of the 41st Regiment on the Civil War Soldiers and Sailors database? It says:
41st Regiment, Virginia Infantry
Overview: 41st Infantry Regiment completed its organization in July, 1861. Men of this unit were recruited in Petersburg and Sussex, Chesterfield, Norfolk, and Nansemond counties. After serving in the Department of Norfolk, it was assigned to General Mahone's and Weisiger's Brigade, Army of Northern Virginia. The 41st fought with the army from Seven Pines to Cold Harbor, then was involved in the Petersburg siege south of the James River and the final campaign at Appomattox. It contained 564 effectives in June, 1862, lost 14 killed, 51 wounded, and 20 missing at Malvern Hill, and 8 killed and 34 wounded at Second Manassas. The unit reported 9 casualties in the Maryland Campaign, 5 at Fredericksburg, and 29 at Chancellorsville. Of the 276 engaged at Gettysburg, five percent were disabled. On April 9, 1865, it surrendered with 10 officers and 99 men. The field officers were Colonels John R. Chambliss, Jr. and William A. Parham, Lieutenant Colonels George Blow, Jr. and Joseph P. Minetree, and Majors William H. Etheredge and Francis W. Smith.
As the regiment lost so many persons it would not be a surprise that Company H was folded into another. But the entries in the database do not say. About the only other thing you might try is to look at the microfilm roll M382 Roll 7.