"No space left on device: AH00023: Couldn't create the mpm-accept mutex" when restarting httpd

This is most likely caused by the semaphore limit of the OS, and Apache not properly cleaning up after itself.

See more details about semaphore limits https://access.redhat.com/documentation/en-us/red_hat_enterprise_linux/5/html/tuning_and_optimizing_red_hat_enterprise_linux_for_oracle_9i_and_10g_databases/sect-oracle_9i_and_10g_tuning_guide-setting_semaphores-setting_semaphore_parameters

Those errors mean that there is a lack of inner-process communication resources in the system, such as semaphores or shared memory segments. Try running next to see if the semaphore limit is reached and see results:

ipcs -s | wc -l

cat /proc/sys/kernel/msgmni

cat /proc/sys/kernel/sem

Execute the following command via SSH or console and see if it helps :

ipcs -s | awk -v user=apache '$3==user {system("ipcrm -s "$2)}'

ipcs -s lists currently used semaphores.

awk -v user=apache filters out the ones, owned by apache user and next part executes icprm -s "id" for each of it which removes that semaphore.

I.e. whole command removes all semaphores owned by apache user

While the answer by @dzup4uk seems to be able to point out what the issue is, in order to actually solve the issue you have to ensure that the semaphores get cleaned up. ipcs command will show what the issue is but in order to actually solve the issue you have to do some cleaning which can be done with

ipcrm -a