Are timing attacks exploitable if each key is used only once? Suppose that one performs (for example) AES-GCM encryption and decryption using an algorithm that is vulnerable to timing attacks, but each key is used only once. Is it still possible to perform a successful timing attack?
Yes. 

Let's a thought experiment and not limit this to AES-GCM.

A very trivial example:

$M = \{0, 1\}$ (a one bit message)

$K = \{0, 1\}$ (a one bit key)

$E(m, k) = m \oplus k$

Let's say with this implementation the computation takes 100x as long if $k = 1$. Running this function only one time will give you a pretty good idea what k is based on how long it takes.

Again, this is just a trivial example meant for a thought experiment as to why you wouldn't necessarily need the encryption process to go more than once.

Another case might be that the plaintext has a series of repeated texts. All of which will be computed against the same key. This can be (not always) similar to computing a single plain text several times.