Savings and loan associations across the country experienced a net gain in deposits of $1.3 billion during August, their second consecutive monthly increase.

Countering the national trend, however, Washington-area thrifts had a net decrease in deposits of $1.2 million in August -- their second straight monthly loss.

James R. Harris, president of the Metropolitan Washington Savings and Loan League, attributed the different trend to the sophistication of area savers. District thrifts have many accounts larger than the national average, he explained. And depositors with $40,000 or $50,000 in their accounts move their money more quickly than do those with $2,000 balances in order to take advantage of higher-paying investments elsewhere.

Yet though withdrawals outpaced deposits at the 16 District and five Maryland thrifts in the league, losses moderated in August. July's net outflow amounted to $5.6 million.

On the national scene, mortgage loans closed last month amounted to $8 billion, up 40 percent over July, although still 18 percent less than a year earlier. This was the largest volume of loans closed since last November.

Locally, the 21 S & Ls concluded $87.1 million in mortgages last month, up from $84.3 in July but still off one-third from last August.

The Federal Home Loan Bank Board reports that nationwide commitments for future mortgage loans amounted to $10.5 billion in August, one-quarter more than July's volume, and 6 percent more than a year ago. The washington area had a different experience as commitments rose in August by just 6 percent to $560.7 million form $533.7 million in July. But they were up one-fourth over August 1979.

FHLBB President Jay Janis termed the August gains "impressive." But he warned that "further increases will be heavely dependent on a continuing improvement in savings inflow, and this will be substantially influenced by changes in market interest rates, which have recently risen further."