Hello from JustAnswer. This is Dr. Love.
Yes, it is possible that you could be pregnant. All urine pregnancy tests are designed to detect the pregnancy hormone, beta-HCG, when it is above a certain threshold. These tests are most sensitive on a morning urine specimen, because that is when the urine is most concentrated and when the beta-HCG levels are most likely to be above the threshold.
It is also true that early in pregnancy, when the beta-HCG levels are just starting to rise, the level could be just above the threshold in the morning, and below the threshold later in the day. As the pregnancy progresses, the beta-HCG levels will rise so that the pregnancy test will be positive throughout the day.
So, if a morning specimen is positive but a test later in the day is negative, it is still very likely that you are pregnant, but early in the pregnancy. If you were to perform the test again tomorrow morning with an early morning urine specimen, then the test will likely be positive again.
If I can provide any additional information, please let me know.