Short answer
Without a hole, water collects in the bottom of the container and roots growing into it sit in water, which is the most common way a potted plant dies. A gravel layer does not fix this and makes it worse. The practical answer is to grow the plant in a plain pot that drains and set that inside the decorative one.
Listed in the order they are worth ruling out. It is normal for more than one of these to be happening at once, so work down the list rather than stopping at the first match.
Without a hole, everything you pour in stays in. The bottom of the container becomes a reservoir, and any root growing down into it sits in water.
What to check first
Tip the container carefully on its side over a sink or a bed. If water runs out, that water has been standing against the roots.
This is worth ruling out because it is the most widely repeated container advice there is, and it does the opposite of what people expect.
What to check first
If you put stones, shards or packing material in the bottom before filling the pot, that layer is where the problem is rather than a fix for it.
Less likely in the first season, and easy to check by eye. In a pot that drains, watering until it runs out of the bottom washes accumulated fertilizer salts away. In a pot with no hole there is nowhere for them to go.
What to check first
Look at the surface of the mix and around the inside of the rim for a white or crusty deposit.
Still not sure
This is exactly what your county Extension office answers, for free. They are the local horticulture experts for your area, they know what is going around this season where you live, and they will look at a photo.
Find your local Extension officePollinator Patch gives you watering and seasonal care for the plants you already own, written for your region rather than for gardening in general.