For starters you can use the tool ethtool to run your NIC's self tests.
excerpt from man page
ethtool -t|--test DEVNAME Execute adapter self test
Example
$ sudo ethtool -t eth0
The test result is PASS
The test extra info:
Register test (offline) 0
Eeprom test (offline) 0
Interrupt test (offline) 0
Loopback test (offline) 0
Link test (on/offline) 0
Looking at the statistics for the NIC may be useful too in terms of diagnosing your issue further.
$ sudo ethtool -S eth0
NIC statistics:
rx_packets: 988097069
tx_packets: 589028032
rx_bytes: 1291674232357
tx_bytes: 116257143322
rx_broadcast: 210375
tx_broadcast: 34690
rx_multicast: 69184
tx_multicast: 179
rx_errors: 0
tx_errors: 0
tx_dropped: 0
multicast: 69184
collisions: 0
rx_length_errors: 0
rx_over_errors: 0
rx_crc_errors: 0
rx_frame_errors: 0
rx_no_buffer_count: 0
rx_missed_errors: 0
tx_aborted_errors: 0
tx_carrier_errors: 0
tx_fifo_errors: 0
tx_heartbeat_errors: 0
tx_window_errors: 0
tx_abort_late_coll: 0
tx_deferred_ok: 0
tx_single_coll_ok: 0
tx_multi_coll_ok: 0
tx_timeout_count: 0
tx_restart_queue: 346104
rx_long_length_errors: 0
rx_short_length_errors: 0
rx_align_errors: 0
tx_tcp_seg_good: 0
tx_tcp_seg_failed: 0
rx_flow_control_xon: 56
rx_flow_control_xoff: 56
tx_flow_control_xon: 0
tx_flow_control_xoff: 0
rx_long_byte_count: 1291674232357
rx_csum_offload_good: 987406053
rx_csum_offload_errors: 3730
rx_header_split: 0
alloc_rx_buff_failed: 0
tx_smbus: 0
rx_smbus: 0
dropped_smbus: 0
rx_dma_failed: 0
tx_dma_failed: 0
Any of the statistics that have the string "error" in them should be zero. If they aren't then I would pursue what may have caused these.