An alternative view maintains that really the prohibition is adding levels of tumah, not just performing an act that would make one tamei.

When one touches a dead body he is tamei for at least 7 days. Thus if a kohein would touch a corpse one day, to touch one the next day would be to increase his levels of tumah because he restarts his 7 day count.

Moreover, one who is in contact with a corpse is on a higher level of tumah than one who had touched one. This rule is called "cherev ke-chalal" and is analyzed in the first perek of the Mishnayot in Ahilot. Basically it means while you are touching you become an extension of the corpse such that anything you are touching (for instance, your clothes) become tamei to the first degree, as opposed to second degree, even though they themselves aren't touching the corpse! Thus a kohein who touched a corpse and let go, would be adding to his level of tumah by touching it again.

It is thus very reasonable to argue that a kohein who is currently touching a corpse has no obligation to let go, as he is not raising his tumah level -- it is already risen.

One could discuss whether touching the corpse for a full day is a violation of adding to the 7 days, as above. This is a matter unresolved in the Achronim.

EDIT:

Here is an excellent post on the issue: http://www.the-daf.com/talmud-conceptual/kohanim-becoming-tamei-nowadays-whats-the-story/

An alternative view maintains that really the prohibition is adding levels of tumah, not just performing an act that would make one tamei.

When one touches a dead body he is tamei for at least 7 days. Thus if a kohein would touch a corpse one day, to touch one the next day would be to increase his levels of tumah because he restarts his 7 day count.

Moreover, one who is in contact with a corpse is on a higher level of tumah than one who had touched one. This rule is called "cherev ke-chalal" and is analyzed in the first perek of the Mishnayot in Ahilot. Basically it means while you are touching you become an extension of the corpse such that anything you are touching (for instance, your clothes) become tamei to the first degree, as opposed to second degree, even though they themselves aren't touching the corpse! Thus a kohein who touched a corpse and let go, would be adding to his level of tumah by touching it again.

It is thus very reasonable to argue that a kohein who is currently touching a corpse has no obligation to let go, as he is not raising his tumah level -- it is already risen.

One could discuss whether touching the corpse for a full day is a violation of adding to the 7 days, as above. This is a matter unresolved in the Achronim.

Here is an excellent post on the issue: Kohanim becoming Tamei Nowadays – What’s the Story?

An alternative view maintains that really the prohibition is adding levels of tumah, not just performing an act that would make one tamei.

When one touches a dead body he is tamei for at least 7 days. Thus if a kohein would touch a corpse one day, to touch one the next day would be to increase his levels of tumah because he restarts his 7 day count.

Moreover, one who is in contact with a corpse is on a higher level of tumah than one who had touched one. This rule is called "cherev ke-chalal" and is analyzed in the first perek of the Mishnayot in Ahilot. Basically it means while you are touching you become an extension of the corpse such that anything you are touching (for instance, your clothes) become tamei to the first degree as opposed to second degree even though they themselves aren't touching the corpse! Thus a kohein who touched a corpse and let go, would be adding to his level of tumah by touching it again.

It is thus very reasonable to argue that a kohein who is currently touching a corpse has no obligation to let go, as he is not raising his tumah level -- it is already risen.

One could discuss whether touching the corpse for a full day is a violation of adding to the 7 days, as above. This is a matter unresolved in the Achronim.

An alternative view maintains that really the prohibition is adding levels of tumah, not just performing an act that would make one tamei.

When one touches a dead body he is tamei for at least 7 days. Thus if a kohein would touch a corpse one day, to touch one the next day would be to increase his levels of tumah because he restarts his 7 day count.

Moreover, one who is in contact with a corpse is on a higher level of tumah than one who had touched one. This rule is called "cherev ke-chalal" and is analyzed in the first perek of the Mishnayot in Ahilot. Basically it means while you are touching you become an extension of the corpse such that anything you are touching (for instance, your clothes) become tamei to the first degree, as opposed to second degree, even though they themselves aren't touching the corpse! Thus a kohein who touched a corpse and let go, would be adding to his level of tumah by touching it again.

It is thus very reasonable to argue that a kohein who is currently touching a corpse has no obligation to let go, as he is not raising his tumah level -- it is already risen.

One could discuss whether touching the corpse for a full day is a violation of adding to the 7 days, as above. This is a matter unresolved in the Achronim.

EDIT:

Here is an excellent post on the issue: http://www.the-daf.com/talmud-conceptual/kohanim-becoming-tamei-nowadays-whats-the-story/