I have a album folder which I have assigned to a usergroup for them to upload pics to it.Now each time I upload a photo to it (or by that new user of group), album gets unpublished. I have to republish the album everytime. How to prevent this so that album does not get unpublished with each upload?

How did you get the album to be unpublished in the first place, Have you selected an option some where? We will probably need a bit more details than you have given. Suggest you read the forum rules post.

Nope..Album was published even when it did not have any images. Also Option to approve album automatically was unchecked but Images should be viewable by default was checked. But as soon as a image gets uploaded to the published album either by me or a user, it gets unpublished and have to publish it manually.

What is the value of t;he show field in the album's database entry?

How are the images getting uploaded?

Those options only change the database default values for the show field. (That is the value assigned when the entry is created.) Otherwise the only place that field gets changed that I am aware of is when you publish/unpublish the album.

[edit] Also, what (if any) filters are active?

I have just run a test on the 1.2.8 RC1 and cannot reproduce the problem.