THE FLC OF A CLBING DEPARTING B737-700 FAILS TO INTERCEPT A90 DURING RADAR VECTORING FROM ZNY; NY.

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DURING CLBOUT FROM EWR ARPT WE WERE INSTRUCTED TO CLB OUT ON A HDG OF 300 DEGS TO AN ALT OF 10000 FT BY DEP. NEXT WE WERE INSTRUCTED BY CTR TO CLB TO FL220 ON A HDG OF 360 DEGS AND INTERCEPT J95 BTWN GAYEL AND STOMP INTXNS. AT THIS TIME I OBSERVED THE CAPT; WHO WAS THE PF; ENTER THE NECESSARY ELEMENTS TO ALLOW THE AUTOPLT TO JOIN THE AIRWAY. BOTH LNAV AND VNAV WERE ENGAGED AND ILLUMINATED. OUR NEXT INSTRUCTION WAS TO INTERCEPT ON A HDG OF 340 DEGS. I ACKNOWLEDGED ZNY. AT THIS TIME I DID NOT REMEMBER IF THE LNAV BUTTON WAS STILL ILLUMINATED. SEVERAL MINS LATER; I RECEIVED A CLRNC FROM ZNY TO CLB AND MAINTAIN FL350. I RESPONDED AND RIGHT AFTER THAT THE CTLR ASKED IF WE WERE IN A L TURN. APPARENTLY; THE LNAV HAD BECOME DISENGAGED. WE THEN WERE INSTRUCTED TO TURN L AND REJOIN THE AIRWAY. I BELIEVE THAT FOR SOME REASON LNAV DISCONNECTED AND WAS NOT OBSERVED WITH THE SECOND HDG CHANGE. AT THE TIME I WAS CHKING THE FUTURE RTE AND NOT FOLLOWING THE ACFT PROGRESS ON A SHORT RANGE SCALE. FOR THAT REASON I WILL NO LONGER LEAVE THE CLOSER RANGE SETTING UNTIL A MORE STABLE ENVIRONMENT HAS BEEN ESTABLISHED.